Mensuration of 2D Shapes - Triangle Problems for Exams

Mensuration of 2D Shapes - Problems on Triangles - Applications

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

A. 10 cm
B. 12 cm
C. 14 cm
D. 16 cm

Solution

Using the Pythagorean theorem, hypotenuse = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.

Correct Answer: A — 10 cm

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Q. A triangle has an area of 30 cm² and a base of 10 cm. What is the height?

A. 6 cm
B. 5 cm
C. 3 cm
D. 4 cm

Solution

Area = 1/2 * base * height. Therefore, height = (2 * Area) / base = (2 * 30) / 10 = 6 cm.

Correct Answer: A — 6 cm

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Q. A triangle has an area of 50 cm² and a base of 10 cm. What is the height?

A. 5 cm
B. 10 cm
C. 8 cm
D. 12 cm

Solution

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

Correct Answer: A — 5 cm

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Q. A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. What is its area?

A. 84 cm²
B. 96 cm²
C. 70 cm²
D. 120 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. A triangle has vertices at (1, 2), (4, 6), and (1, 6). What is the area of the triangle?

A. 6 cm²
B. 8 cm²
C. 10 cm²
D. 12 cm²

Solution

Area = 1/2 * |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)| = 1/2 * |1(6-6) + 4(6-2) + 1(2-6)| = 1/2 * |0 + 16 - 4| = 1/2 * 12 = 6 cm².

Correct Answer: A — 6 cm²

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Q. If the area of a triangle is 36 cm² and the base is 12 cm, what is the height?

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

Solution

Area = 1/2 * base * height. Therefore, height = (2 * Area) / base = (2 * 36) / 12 = 6 cm.

Correct Answer: A — 6 cm

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Q. If the lengths of the sides of a triangle are in the ratio 3:4:5 and the perimeter is 60 cm, what is the length of the longest side?

A. 20 cm
B. 15 cm
C. 25 cm
D. 30 cm

Solution

Let the sides be 3x, 4x, 5x. Then, 3x + 4x + 5x = 60. Therefore, 12x = 60, x = 5. Longest side = 5x = 25 cm.

Correct Answer: A — 20 cm

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Q. If the lengths of two sides of a triangle are 8 cm and 15 cm, and the included angle is 60 degrees, what is the area?

A. 60 cm²
B. 80 cm²
C. 90 cm²
D. 100 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 the perimeter of an equilateral triangle is 36 cm, what is the length of one side?

A. 10 cm
B. 12 cm
C. 9 cm
D. 15 cm

Solution

Perimeter = 3 * side. Therefore, side = Perimeter / 3 = 36 / 3 = 12 cm.

Correct Answer: B — 12 cm

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Q. In a triangle, if one angle is 90 degrees and the other two angles are 45 degrees each, what is the area if the legs are 5 cm each?

A. 12.5 cm²
B. 25 cm²
C. 20 cm²
D. 15 cm²

Solution

Area = 1/2 * base * height = 1/2 * 5 * 5 = 12.5 cm².

Correct Answer: A — 12.5 cm²

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Q. In a triangle, if one angle is 90 degrees and the other two angles are 45 degrees each, what is the area if the length of each leg is 5 cm?

A. 12.5 cm²
B. 25 cm²
C. 20 cm²
D. 15 cm²

Solution

Area = 1/2 * base * height = 1/2 * 5 * 5 = 12.5 cm².

Correct Answer: B — 25 cm²

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Q. What is the circumradius of a triangle with sides 5 cm, 12 cm, and 13 cm?

A. 6.5 cm
B. 7 cm
C. 8 cm
D. 5 cm

Solution

For a right triangle, circumradius R = hypotenuse / 2 = 13 / 2 = 6.5 cm.

Correct Answer: B — 7 cm

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Q. What is the height of a triangle with a base of 8 cm and an area of 32 cm²?

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

Solution

Area = 1/2 * base * height. Therefore, height = (2 * Area) / base = (2 * 32) / 8 = 8 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 10 cm in an isosceles triangle with equal sides of 13 cm?

A. 12 cm
B. 10 cm
C. 9 cm
D. 8 cm

Solution

Using Pythagorean theorem: altitude = √(13² - (10/2)²) = √(169 - 25) = √144 = 12 cm.

Correct Answer: D — 8 cm

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Showing 1 to 14 of 14 (1 Pages)

Mensuration of 2D Shapes - Problems on Triangles - Applications

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