Mensuration of 2D Shapes - Triangle Problems for Exams

Mensuration of 2D Shapes - Problems on Triangles - Problem Set

Q. A triangle has two sides measuring 6 cm and 8 cm. If the included angle is 60 degrees, what is the area of the triangle?

A. 24 cm²
B. 18 cm²
C. 20 cm²
D. 30 cm²

Solution

Area = 1/2 * a * b * sin(C) = 1/2 * 6 * 8 * sin(60°) = 24√3/2 = 20.78 cm² (approximately 18 cm²).

Correct Answer: B — 18 cm²

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Q. A triangle has two sides measuring 8 cm and 15 cm. If the included angle 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 an area of 24 cm² and a base of 8 cm, what is the height?

A. 6 cm
B. 8 cm
C. 4 cm
D. 3 cm

Solution

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

Correct Answer: A — 6 cm

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Q. If the angles of a triangle are 30°, 60°, and 90°, and the shortest side is 5 cm, what is the length of the longest side?

A. 10 cm
B. 5√3 cm
C. 5 cm
D. 15 cm

Solution

In a 30-60-90 triangle, the longest side (hypotenuse) is twice the shortest side: 2 * 5 = 10 cm.

Correct Answer: A — 10 cm

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Q. If the base of a triangle is doubled and the height remains the same, how does the area change?

A. It doubles
B. It triples
C. It remains the same
D. It halves

Solution

Area = 1/2 * base * height; if base is doubled, area = 1/2 * (2 * base) * height = 2 * (1/2 * base * height).

Correct Answer: A — It doubles

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Q. If the lengths of the sides of a triangle are 3 cm, 4 cm, and 5 cm, what is its perimeter?

A. 12 cm
B. 15 cm
C. 10 cm
D. 8 cm

Solution

Perimeter = 3 + 4 + 5 = 12 cm.

Correct Answer: A — 12 cm

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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?

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 a right triangle, if one leg is 5 cm and the other leg is 12 cm, what is the length of the hypotenuse?

A. 13 cm
B. 10 cm
C. 15 cm
D. 12 cm

Solution

Using Pythagorean theorem: hypotenuse = √(5² + 12²) = √(25 + 144) = √169 = 13 cm.

Correct Answer: A — 13 cm

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Q. In a right triangle, if one leg is 9 cm and the other leg is 12 cm, what is the length of the hypotenuse?

A. 15 cm
B. 13 cm
C. 10 cm
D. 14 cm

Solution

Using Pythagorean theorem: hypotenuse = √(9² + 12²) = √(81 + 144) = √225 = 15 cm.

Correct Answer: B — 13 cm

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Q. What is the semi-perimeter of a triangle with sides 7 cm, 8 cm, and 9 cm?

A. 12 cm
B. 14 cm
C. 16 cm
D. 18 cm

Solution

Semi-perimeter = (7 + 8 + 9) / 2 = 24 / 2 = 12 cm.

Correct Answer: B — 14 cm

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Q. What is the semi-perimeter of a triangle with sides measuring 7 cm, 8 cm, and 9 cm?

A. 12 cm
B. 14 cm
C. 16 cm
D. 18 cm

Solution

Semi-perimeter = (7 + 8 + 9) / 2 = 24 / 2 = 12 cm.

Correct Answer: B — 14 cm

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Mensuration of 2D Shapes - Problems on Triangles - Problem Set

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