Mensuration of 2D Shapes - Triangle Problems for Exams

Mensuration of 2D Shapes - Problems on Triangles

Q. A right triangle has legs of lengths 6 cm and 8 cm. What is the area of the triangle?

A. 24 cm²
B. 30 cm²
C. 48 cm²
D. 36 cm²

Solution

Area = 1/2 * base * height = 1/2 * 6 * 8 = 24 cm².

Correct Answer: A — 24 cm²

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Q. A triangle has an area of 48 cm² and a base of 8 cm. What is the height?

A. 12 cm
B. 6 cm
C. 8 cm
D. 10 cm

Solution

Area = 1/2 * base * height. Therefore, 48 = 1/2 * 8 * height. Solving gives height = 48 / 4 = 12 cm.

Correct Answer: B — 6 cm

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Q. A triangle has sides of lengths 9 cm, 12 cm, and 15 cm. Is it a right triangle?

A. Yes
B. No
C. Cannot be determined
D. Only if angles are known

Solution

Yes, because 9² + 12² = 81 + 144 = 225 = 15².

Correct Answer: A — Yes

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Q. A triangle has vertices at (0, 0), (4, 0), and (0, 3). What is its area?

A. 6 cm²
B. 12 cm²
C. 8 cm²
D. 10 cm²

Solution

Area = 1/2 * base * height = 1/2 * 4 * 3 = 6 cm².

Correct Answer: A — 6 cm²

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Q. If a triangle has an area of 36 cm² and a base of 9 cm, what is its height?

A. 8 cm
B. 6 cm
C. 4 cm
D. 10 cm

Solution

Area = 1/2 * base * height. 36 = 1/2 * 9 * height. Height = (36 * 2) / 9 = 8 cm.

Correct Answer: B — 6 cm

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Q. If the lengths of the sides of a triangle are 5 cm, 12 cm, and 13 cm, what type of triangle is it?

A. Acute
B. Obtuse
C. Right
D. Equilateral

Solution

Since 5² + 12² = 13², it is a right triangle.

Correct Answer: C — Right

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Q. If the lengths of two sides of a triangle are 5 cm and 12 cm, and the included angle is 90 degrees, what is the area?

A. 30 cm²
B. 60 cm²
C. 24 cm²
D. 20 cm²

Solution

Area = 1/2 * side1 * side2 = 1/2 * 5 * 12 = 30 cm².

Correct Answer: A — 30 cm²

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Q. If the sides of a triangle are 7 cm, 24 cm, and 25 cm, what is its area?

A. 84 cm²
B. 96 cm²
C. 120 cm²
D. 72 cm²

Solution

Using Heron's formula, s = (7 + 24 + 25)/2 = 28. Area = √(s(s-a)(s-b)(s-c)) = √(28(28-7)(28-24)(28-25)) = √(28*21*4*3) = 84 cm².

Correct Answer: B — 96 cm²

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Q. In a right triangle, if one leg is 6 cm and the other leg is 8 cm, what is the area?

A. 24 cm²
B. 30 cm²
C. 48 cm²
D. 36 cm²

Solution

Area = 1/2 * leg1 * leg2 = 1/2 * 6 * 8 = 24 cm².

Correct Answer: A — 24 cm²

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Q. What is the area of an isosceles triangle with a base of 10 cm and equal sides of 13 cm?

A. 60 cm²
B. 65 cm²
C. 70 cm²
D. 75 cm²

Solution

Using Heron's formula, s = (10 + 13 + 13) / 2 = 18. Area = √(s(s-a)(s-b)(s-c)) = √(18(18-10)(18-13)(18-13)) = √(18*8*5*5) = 60 cm².

Correct Answer: B — 65 cm²

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Q. What is the height of a triangle with an area of 60 cm² and a base of 12 cm?

A. 10 cm
B. 5 cm
C. 8 cm
D. 6 cm

Solution

Area = 1/2 * base * height. Therefore, 60 = 1/2 * 12 * height. Height = 60 / 6 = 10 cm.

Correct Answer: D — 6 cm

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Q. What is the length of the altitude to the base of a triangle with an area of 50 cm² and a base of 10 cm?

A. 10 cm
B. 5 cm
C. 15 cm
D. 20 cm

Solution

Area = 1/2 * base * height. 50 = 1/2 * 10 * height. Height = (50 * 2) / 10 = 10 cm.

Correct Answer: B — 5 cm

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Mensuration of 2D Shapes - Problems on Triangles

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