Mensuration of 2D Shapes - Triangle Problems for Exams

Mensuration of 2D Shapes - Problems on Triangles - Case Studies

Q. A triangle has angles measuring 30°, 60°, and 90°. If the shortest side is 5 cm, what is the area?

A. 12.5 cm²
B. 15 cm²
C. 10 cm²
D. 20 cm²

Solution

Area = 1/2 * base * height. Height = 5 * sin(60°) = 5 * (√3/2) = 5√3/2. Area = 1/2 * 5 * (5√3/2) = 12.5 cm².

Correct Answer: A — 12.5 cm²

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Q. A triangle has sides of lengths 5 cm, 12 cm, and 13 cm. Is this triangle a right triangle?

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

Solution

Yes, because 5² + 12² = 25 + 144 = 169 = 13².

Correct Answer: A — Yes

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Q. A triangle has two sides measuring 8 cm and 15 cm. If the angle between them is 60 degrees, what is the area of the triangle?

A. 60 cm²
B. 30 cm²
C. 40 cm²
D. 70 cm²

Solution

Area = 1/2 * a * b * sin(C) = 1/2 * 8 * 15 * sin(60°) = 60 cm².

Correct Answer: A — 60 cm²

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Q. If a triangle has a base of 15 cm and a height of 10 cm, what is the area?

A. 75 cm²
B. 150 cm²
C. 100 cm²
D. 50 cm²

Solution

Area = 1/2 * base * height = 1/2 * 15 * 10 = 75 cm².

Correct Answer: A — 75 cm²

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

A. 84 cm²
B. 168 cm²
C. 42 cm²
D. 56 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: A — 84 cm²

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

A. 56 cm
B. 50 cm
C. 45 cm
D. 30 cm

Solution

Perimeter = 7 + 24 + 25 = 56 cm.

Correct Answer: B — 50 cm

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Q. In an equilateral triangle with a side length of 6 cm, what is the area?

A. 9√3 cm²
B. 12 cm²
C. 18 cm²
D. 36 cm²

Solution

Area = (√3/4) * side² = (√3/4) * 6² = 9√3 cm².

Correct Answer: A — 9√3 cm²

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Q. What is the height of a triangle with an area of 36 cm² and a base of 12 cm?

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

Solution

Area = 1/2 * base * height; 36 = 1/2 * 12 * height; height = 36 / 6 = 6 cm.

Correct Answer: A — 6 cm

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Q. What is the length of the altitude from the vertex opposite the base of a triangle with a base of 10 cm and an area of 40 cm²?

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

Solution

Area = 1/2 * base * height. 40 = 1/2 * 10 * height. Height = (40 * 2) / 10 = 8 cm.

Correct Answer: B — 6 cm

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Q. What is the semi-perimeter of a triangle with sides 10 cm, 14 cm, and 16 cm?

A. 20 cm
B. 25 cm
C. 30 cm
D. 22 cm

Solution

Semi-perimeter = (10 + 14 + 16) / 2 = 40 / 2 = 20 cm.

Correct Answer: B — 25 cm

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Mensuration of 2D Shapes - Problems on Triangles - Case Studies

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