Question 1

The diagonals of a rhombus are 10 cm and 24 cm. Find its area.

Accepted Answer

Area of rhombus = (1/2) × d₁ × d₂ = (1/2) × 10 × 24 = 120 cm².

Question 2

Two parallel lines are cut by a transversal. If one of the alternate interior angles is 65°, what is the measure of the other alternate interior angle?

Accepted Answer

Alternate interior angles are equal when two parallel lines are cut by a transversal.

Question 3

The area of a circle is 154 cm². What is its circumference? (Use π = 22/7)

Accepted Answer

From A = πr², we get 154 = (22/7) × r², so r² = 49 and r = 7 cm; then C = 2πr = 2 × (22/7) × 7 = 44 cm.

Question 4

A parallelogram has a base of 12 cm and a height of 8 cm. What is its area?

Accepted Answer

Area of parallelogram = base × height = 12 × 8 = 96 cm².

Question 5

In a right-angled triangle, the two legs are 5 cm and 12 cm. What is the length of the hypotenuse?

Accepted Answer

Using Pythagoras theorem: hypotenuse² = 5² + 12² = 25 + 144 = 169, so hypotenuse = 13 cm.

Question 6

In a trapezium, the parallel sides are 6 cm and 14 cm, and the height is 5 cm. What is its area?

Accepted Answer

Area of trapezium = (1/2) × (sum of parallel sides) × height = (1/2) × (6 + 14) × 5 = 50 cm².

Question 7

A triangle has a base of 12 cm and a height of 8 cm. What is its area?

Accepted Answer

Area of triangle = (1/2) × base × height = (1/2) × 12 × 8 = 48 cm².

Question 8

A circle has a radius of 10 cm. What is its area? (Use π = 3.14)

Accepted Answer

Area = πr² = 3.14 × 10² = 3.14 × 100 = 314 cm².

Question 9

A cylinder has radius 7 cm and height 10 cm. What is its total surface area?

Accepted Answer

Total surface area of cylinder = 2πr(r + h) = 2 × 22/7 × 7 × (7 + 10) = 2 × 22 × 17 = 748 cm².

Question 10

Two lines intersect and form four angles. If one of the angles is 48°, what is the measure of its vertically opposite angle?

Accepted Answer

Vertically opposite angles are always equal.

Question 11

A transversal crosses two parallel lines. If one of the corresponding angles measures 72°, what is the measure of the other corresponding angle?

Accepted Answer

Corresponding angles are equal when a transversal cuts two parallel lines.

Question 12

A cone has base radius 6 cm and slant height 10 cm. What is its curved surface area?

Accepted Answer

Curved surface area of cone = πrl = 22/7 × 6 × 10 = 1320/7 ≈ 188.6 cm², but using π ≈ 3: πrl = 3 × 6 × 10 = 180 cm².

Question 13

A rectangular prism has length 8 cm, width 5 cm, and height 6 cm. What is its total surface area?

Accepted Answer

Surface area of rectangular prism = 2(lw + wh + lh) = 2(8×5 + 5×6 + 8×6) = 2(40 + 30 + 48) = 236 cm².

Question 14

A pyramid has a square base with side length 10 cm and height 12 cm. What is its volume?

Accepted Answer

Volume of pyramid = (1/3) × base area × height = (1/3) × 10² × 12 = (1/3) × 100 × 12 = 400 cm³.

Question 15

A triangular prism has a triangular base with area 24 cm² and the prism's length is 9 cm. What is its volume?

Accepted Answer

Volume of prism = base area × length = 24 × 9 = 216 cm³.

Question 16

A sphere has radius 5 cm. What is its volume? (Use π = 22/7)

Accepted Answer

Volume of sphere = 4/3 πr³ = 4/3 × 22/7 × 5³ = 4/3 × 22/7 × 125 = 2750/3 cm³.

Question 17

An equilateral triangle has a side length of 6 cm. What is the sum of all its interior angles?

Accepted Answer

The sum of interior angles in any triangle is always 180°, regardless of the type or side lengths.

Question 18

The circumference of a circle is 44 cm. What is its radius? (Use π = 22/7)

Accepted Answer

Using C = 2πr, we get 44 = 2 × (22/7) × r, so r = 44 × 7 / 44 = 7 cm.

Question 19

The volume of a sphere is 288π cm³. What is its radius?

Accepted Answer

Volume of sphere = (4/3)πr³; solving 288π = (4/3)πr³ gives r³ = 216, so r = 6 cm.

Question 20

A cone has base radius 6 cm and slant height 10 cm. Find its total surface area.

Accepted Answer

Total surface area of cone = πr² + πrl = πr(r + l) = (22/7) × 6 × (6 + 10) = 288 cm².

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