Geometry MCQs with Answers – Solved from Past Papers
74 solved Geometry MCQs collected from real PPSC, FPSC, SPSC, KPPSC, BPSC & NTS past papers (2006–2026). Tap an option to attempt — see correct answer instantly. Download the full PDF for offline revision.
The area of a triangle is 126 cm² and its base is 28 cm. Find its height?
Show solution
Area = ½ × base × height, so 126 = ½ × 28 × h, giving 126 = 14h, hence h = 9 cm.
How many square feet are in one acre?
Show solution
1 acre = 43,560 square feet by standard definition (66 ft × 660 ft = 43,560 sq ft).
lf each interior angle of a polygon is 162°, calculate the number of sides?
Show solution
Each interior angle of a regular polygon = (n−2)×180°/n = 162°. Solving: 180n − 360 = 162n → 18n = 360 → n = 20.
A parallelogram has a side 15 cm and 10 cm find it’s perimeter…… cm²
Show solution
Perimeter of a parallelogram = 2(a+b) = 2(15+10) = 2×25 = 50 cm.
Area of equilateral triangle is V243/16, find the length of side of triangle?
If each interior angle of a polygon is 162°, calculate the number of sides?
Show solution
(n−2)×180°/n = 162° gives n = 20 (same as item 2).
Aparallelogram has a side 15 cm and 10 cm find it's perimeter……. cm²
Show solution
Perimeter = 2(15+10) = 50 cm.
If ABCD is a square with given points A(2,3), B(-2,2), C(-1,-2), then what are the coordinates of D?
Show solution
For square ABCD, D = A + C − B = (2+(−1)−(−2), 3+(−2)−2) = (3, −1).
The angle of elevation of the top of a tower from a point 20 m away from its base is 45°. What is the height of the tower?
Show solution
tan(45°) = h/20 = 1, so h = 20 m.
Ifthe side of a square is 5 units, what is its area?
Show solution
Area of square = s² = 5² = 25 sq units.
The area of a rectangular field is 17 m by 13 m. If the cost of tiling is 70 per square meter, what is the total cost of tiling the field?
Show solution
Area = 17 × 13 = 221 m². Cost = 221 × 70 = Rs. 15,470.
How many tangents can be drawn toa circle in total?
Show solution
From any external point or considering all points outside, infinitely many tangents can be drawn to a circle in total.
A square park has a side of 50 meters. If the rate of fencing is Rs. 8 per meter, what is the total cost of fencing the park?
Show solution
Perimeter = 4×50 = 200 m. Cost = 200 × 8 = Rs. 1,600.
Ifthe area of rectangle is 30cm² and width is 5 cm find the length?
Show solution
Area = L×W → 30 = L×5 → L = 6 cm.
If one angle of a parallelogram is 24° less than twice the smallest angle, then the largest angle of the parallelogram is?
Show solution
Let smallest angle = x. Adjacent angles in a parallelogram are supplementary: x + (2x−24) = 180 → 3x = 204 → x = 68°. Largest = 180−68 = 112°.
Two concentric circles are of radii 10 cm and 6 cm. Find the length of the chord of the larger circle which touches the smaller circle?
Show solution
Chord touching inner circle is perpendicular to radius at tangent point. Half-chord = √(10²−6²) = √64 = 8. Chord = 16 cm.
378 trees are planted in rows in the shape of an isosceles triangle, the numbers in successive rows decreasing by one from the base to the top. How many trees are there in the row which forms the base of the triangle?
Show solution
Sum of n consecutive integers from k down to (k−n+1) = 378. Try base = 27: 1+2+…+27 = 27×28/2 = 378. So base row = 27.
One fifth of the sum of two angles is 24 degree and half of their difference is 14 degree. Calculate the largest angle?
Show solution
Sum = 5×24 = 120; difference = 2×14 = 28. Larger = (120+28)/2 = 74°.
Find the breadth of a rectangular field whose length is 18 m and area is 216 m²?
Show solution
W = Area/L = 216/18 = 12 m.
Find the breadth of a rectangular field, given that its length is 18 meters and its area is 666 square meters?
Show solution
W = 666/18 = 37 m.
How many bricks each of volume 750cm² will be required to construct a wall 10m, 5m, 30cm²
Show solution
Wall volume = 1000 × 500 × 30 = 15,000,000 cm³. Bricks = 15,000,000 / 750 = 20,000.
Find the square root of 6084 is?
Show solution
78² = 6084, so √6084 = 78.
Three angles of a quadrilateral measure 68°, 85°, and 95°. Find the measure of the fourth angle?
Show solution
Quadrilateral angles sum to 360°. Fourth = 360 − (68+85+95) = 360 − 248 = 112°.
The base and height of a triangle are (x+3) cm and (2x-5) cm respectively. If the area of the triangle is 20 cm²?
Show solution
½(x+3)(2x−5) = 20 → (x+3)(2x−5) = 40 → 2x²+x−15 = 40 → 2x²+x−55 = 0. x = 5 works: 2(25)+5−55 = 0.
The inner circumference of a circular race track is 440m. If the width of track is 14m, what is the radius of outer circle?
Show solution
Inner circumference 2πr = 440 → r = 440×7/(2×22) = 70 m. Outer = 70+14 = 84 m.
The angles of a triangle are (x-35), (x- 25) and (1/2x-10), find x?
Show solution
Sum of triangle angles = 180°: (x−35)+(x−25)+(x/2−10) = 180 → 2.5x − 70 = 180 → 2.5x = 250 → x = 100.
The area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides?
Show solution
This is the statement of the Pythagorean theorem.
Ifthe radius of circle is 1 cm then its area in mm² is?
Show solution
r = 1 cm = 10 mm. Area = π × 10² = 100π ≈ 314 mm².
The sum of the squares of two positive integers is 100 and their difference of their square is 28. The sum of the numbers is?
Show solution
a²+b² = 100, a²−b² = 28 → a² = 64, b² = 36 → a = 8, b = 6. Sum = 14.
Arectangular lawn 80 meters by 60 meters has two roads each 10 m wide running in the middle of it, one parallel to the length and the other parallel to the breadth. Find the cost of gravelling at the Rate 30 per square meter?
Show solution
Area of two roads = 80×10 + 60×10 − 10×10 = 800+600−100 = 1300 m². Cost = 1300×30 = Rs. 39,000.
The Angle of elevation of sun when the length of shadow of tree is equal to height of tree?
Show solution
tan θ = height/shadow = 1, so θ = 45°.
The square root of 729 is?
Show solution
27² = 729, so √729 = 27.
The square of standard deviation is called?
Show solution
By definition, variance = (standard deviation)².
A Mason fixed black tiles of square shape around a square room. There are 21 tiles on each side of the room. How many tiles did he need altogether?
Show solution
Border tiles around a square with 21 per side = 4×21 − 4 (corners counted twice) = 84 − 4 = 80 tiles.
The circumference of a circle whose diameter is 7 inches is approximately?
Show solution
Circumference = πd = (22/7)×7 = 22 inches.
If one of the angles of a triangle is 90 degrees what would be the value of other two angles?
Show solution
Other two angles sum to 180−90 = 90°.
294 is multiplied to which positive to give a complete square?
Show solution
294 = 2 × 3 × 7². To make a perfect square, multiply by 2×3 = 6. Then 294×6 = 1764 = 42².
Which one of the following is a positive square root of 2209?
Show solution
47² = 2209, so √2209 = 47.
A ladder makes an angle of 60 degree with the ground against a wall. If the foot of ladder 2m away from the wall. The length of ladder is?
Show solution
cos(60°) = adjacent/hypotenuse = 2/L → L = 2/0.5 = 4 m.
Find the volume of a cuboid having 3 cm length, 3 cm width and 3 cm height?
Show solution
Volume of cube = 3³ = 27 cm³.
When a triangle has two congruent sides, it is called triangle?
Show solution
A triangle with two congruent sides is called isosceles.
Asquare region has an area of 2304 m.Find its perimeter?
Show solution
Side = √2304 = 48 m. Perimeter = 4×48 = 192 m.
How many tiles of dimension 10 square inch are required to cover a floor of dimension of 5 feet by 4 feet?
Show solution
Floor = 5×4 = 20 sq ft = 20×144 = 2880 sq in. Tiles = 2880/10 = 288.
What is the sum of all angles of a triangle?
Show solution
Sum of angles of a triangle = 180°.
The number of square tiles 3" long required to cover a rectangular floor of 30 feet x 40 feet is?
Show solution
Floor = 30×12 × 40×12 = 360×480 in² = 172,800 in². Tile = 3×3 = 9 in². Tiles = 172,800/9 = 19,200.
The length of a rectangle is 3 cm more than its width, if length is 37 cm, the perimeter of rectangle will be?
Show solution
Width = 37−3 = 34. Perimeter = 2(37+34) = 2×71 = 142 cm.
Find the radius of a circle whose circumference is 308 m²
Show solution
2πr = 308 → r = 308×7/(2×22) = 2156/44 = 49 m.
Arectangular carpet has an area of 120 square meters and a perimeter of 46 meters. The length of its diagonal is? 17m Solution: Let length = L and breadth = W Area =LW=120 Perimeter = 2(L+W) = 46 L+W=23 (L+ W)? = L? + W? + 2LW 23? = L? + W? + 2(120) 529 = L? + W? +240 L? + W? = 289 Diagonal? = L? + W?
Show solution
L+W=23, LW=120. L²+W² = 23² − 2(120) = 529−240 = 289. Diagonal² = 289 (so diagonal = 17 m).
Arectangle measures 8cm on length and its diagonal measures 10cm. What is the perimeter of the rectangle?
Show solution
Width = √(10²−8²) = √36 = 6 cm. Perimeter = 2(8+6) = 28 cm.
Diameter of a circle having radius r is?
Show solution
Diameter = 2 × radius = 2r.
Square of 32 is?
Show solution
32² = 1024.
Find the measure of an angle, if six times its complement is 12° less than twice its supplement?
Show solution
6(90−x) = 2(180−x) − 12 → 540−6x = 348−2x → 192 = 4x → x = 48°.
If length of a side of a square is 4cm calculate its area?
Show solution
Area = 4² = 16 cm².
If perpendicular of a triangle is 20 and base is 12 then its area is?
Show solution
Area = ½ × 20 × 12 = 120.
If acube has 3 inches width, 3 inches length and 3 inches height, what would be the volume (in cubic inches) of the cube?
Show solution
Volume = 3³ = 27 cubic inches.
Calculate the perimeter of a rhombus with each side equal to 6cm²
Show solution
Rhombus perimeter = 4×side = 4×6 = 24 cm.
Acube has a volume of 8 cubic meters. If each side is doubled in length what will its new volume be in cubic meters?
Show solution
Original side = 8^(1/3) = 2 m. Doubled = 4 m. New volume = 4³ = 64 m³.
If length 3 Inch, width is 3 inch height 3 inch than tell the volume?
Show solution
Volume = 3×3×3 = 27 cubic inches.
The least number by which 294 must be multiplied to make it a perfect square is?
Show solution
294 = 2 × 3 × 7². Multiply by 6 (=2×3) to make perfect square (1764 = 42²).
Asquare shaped wedding hall has an area of 18m7?. Find the cost of tile WHATSAPP FOR IN CLASSES NITH SIR TAUQEER flooring at the rate of Rs. 725 per square meter?
Two angles are supplementary. One angle is 12° less than three times the other. What is the measure of the larger angle?
Show solution
Let other = x. (3x−12) + x = 180 → 4x = 192 → x = 48°. Larger = 3(48)−12 = 132°.
The square root of 729 is?
Show solution
27² = 729.
Arectangular field is to be fenced on 3 sides leaving a side of 20 feet PREPARATION WI unfenced. If the area of the field is 680 Sq. feet how many feet of fencing will be required?
Show solution
Let width=W. Area = 20×W = 680 → W = 34. Fencing = 20 + 2×34 = 88 feet.
Which one of the following shapes has four equal sides and right angles?
Show solution
A square has four equal sides and four right angles.
Arectangular field which is twice as long as it is broad, has an area of 14450 sqm. What is its perimeter? 510 m Solution: Let breadth =bm Then length = 2b m Area = length x breadth 2b xb = 14450 2b? = 14450 b?
Show solution
2b² = 14450 → b² = 7225 (b = 85, length = 170, perimeter = 510 m).
1square foot is equal to?
Show solution
1 ft = 12 in, so 1 sq ft = 12² = 144 sq inches.
The sum of a positive integer and its square is 2450. The positive integer is?
Show solution
n + n² = 2450 → n² + n − 2450 = 0 → n = (−1+√(1+9800))/2 = (−1+99)/2 = 49.
Find the square of 35?
Show solution
35² = 1225.
Arectangle has a length of 10cm & a perimeter of 30cm. Find the width of the rectangle?
Show solution
P = 2(L+W) → 30 = 2(10+W) → W = 5 cm.
Awire inthe form of a circle of radius 42 cm is cut and bent in the form of a square thus formed is?
Show solution
Wire length = circumference = 2π×42 = 2×(22/7)×42 = 264 cm. Square side = 264/4 = 66 cm.
Arectangle has a length of 10cm anda perimeter of 30cm. Find the width of the rectangle?
Show solution
30 = 2(10+W) → W = 5 cm.
Arectangle has a perimeter of 50 meters. If its length is 13 metres more than its breadth, then its area is?
Show solution
2(L+B)=50 → L+B=25. L = B+13 → 2B+13=25 → B=6, L=19. Area = 19×6 = 114 m².
The square root of 169 is?
Show solution
13² = 169, so √169 = 13.
66 cubic centimeters of silver is drawn into a wire 1 mm in diameter. The length of the wire in meters will be?
Show solution
Wire is a cylinder. r = 0.05 cm. Volume = πr²h → 66 = (22/7)(0.0025)h → h = 66×7/(22×0.0025) = 462/0.055 = 8400 cm = 84 m.
Geometry MCQs for PPSC, FPSC, NTS & All Pakistani Competitive Exams
Geometry is one of the highest-frequency topics in Pakistani competitive exam Math. From PPSC Lecturer, Sub-Inspector and Tehsildar tests to FPSC CSS Screening (MPT), NTS NAT/GAT, OTS, CTS, KPPSC, SPSC, BPSC and AJKPSC — almost every paper contains 1 to 5 geometry questions. Mastering this one topic alone can secure 2–5 marks in any One Paper format exam because most questions test the same handful of area, perimeter, angle and volume formulas.
QuizWing has compiled 74 verified geometry MCQs from real past papers spanning 2006–2026 — every question solved from scratch by AI and answer keys verified. The bank covers area & perimeter (triangles, rectangles, circles, polygons), interior & exterior angles, volume & surface area of solids (cube, cuboid, cylinder, sphere, cone), and coordinate-geometry distance problems.
What types of geometry questions appear?
- Area & perimeter — “Area of triangle is 126 cm² and base is 28 cm; find height” → 9 cm
- Polygon angles — “Each interior angle of a polygon is 162°; find number of sides” → 20
- Circle properties — radius, diameter, circumference, area, chords, tangents
- Pythagoras theorem — right-triangle hypotenuse / missing leg
- Volume & surface area — cube, cuboid, cylinder, sphere, cone problems
- Unit conversion — sq ft to acre (43,560 sq ft = 1 acre), cm³ to m³, etc.
Key geometry formulas
Mental-math shortcuts
- Memorise key constants — π ≈ 3.14 (or 22/7 for rational answers), √2 ≈ 1.414, √3 ≈ 1.732
- 1 acre = 43,560 sq ft, 1 hectare = 10,000 m², 1 km² = 100 hectares
- Regular polygon shortcut — exterior angle = 360° ÷ n; if each interior = X°, then n = 360 ÷ (180 − X)
- Common Pythagorean triples — memorise 3-4-5, 5-12-13, 8-15-17, 7-24-25, 20-21-29
- Equilateral triangle — area = (√3 ÷ 4) × side² ≈ 0.433 × side²
- Diagonal of square = side × √2; diagonal of cube = side × √3
How to use this page for revision
Quiz mode: Tap any option — green = correct, red = wrong. Use the pagination buttons to move between sets of 25 MCQs at a time.
PDF download: Click Download PDF in the sticky bar to grab all 74 MCQs with answers for offline study.
Mixed practice: attempt our full PPSC Mock Test with all subjects + weighted distribution to simulate the real exam.
Geometry weightage by exam
| Exam | Typical Geometry MCQs | Marks Share |
|---|---|---|
| PPSC One Paper | 1–3 | 2–5 |
| FPSC Screening | 2–5 | 4–8 |
| NTS NAT / GAT | 3–6 | 5–10 |
| CSS Screening (MPT) | 3–6 | 6–12 |
| OTS / CTS | 2–4 | 3–7 |
| SPSC / KPPSC / BPSC | 1–3 | 2–5 |
All MCQs sourced from official past papers of PPSC, FPSC, SPSC, KPPSC and NTS. Found a wrong answer? WhatsApp 0302-1417839 — we fix every reported issue within 24 hours.
Frequently Asked Questions
Typically 1 to 3 geometry MCQs appear in every PPSC One Paper test (Sub-Inspector, Tehsildar, Junior Clerk, Lecturer, BPS-14/16/17). FPSC, NTS and CSS papers tend to include 2–5. Mastering this topic alone secures 2–5 guaranteed marks because most questions reduce to the same area, perimeter, angle and volume formulas.
Based on our analysis of 74 past-paper MCQs (2006–2026), the three most-recurring types are: (1) area of triangle / rectangle / circle, (2) polygon interior angle problems, and (3) volume & surface area of cube, cylinder and sphere.
No. Calculators are not allowed in PPSC, FPSC, NTS, OTS or any provincial commission exam. Practise mental math shortcuts — 10%, 25%, 50% calculations should take under 5 seconds.
Yes for PPSC and FPSC — 0.25 marks deducted per wrong answer. Strategy: if you can eliminate 2 out of 4 options confidently, attempt it; otherwise leave blank.
Yes — click the Download PDF button in the sticky bar at the top of the quiz section. You get all 74 MCQs with answers in a branded QuizWing PDF, free, no signup.
Yes — 100% transferable. All provincial public service commissions follow a near-identical Math syllabus. The same geometry MCQs appear (often verbatim) in SPSC, KPPSC, BPSC, AJKPSC and NTS NAT/GAT papers.
Message us on WhatsApp at 0302-1417839 with the question number and what you believe the correct answer should be. We verify against multiple sources and fix every reported issue within 24 hours.