Question 1

A triangle has a base of 16 cm and a height of 12 cm. What is its area?

Accepted Answer

Step 1: Recall the formula for the area of a triangle: Area = (1/2) × base × height. Step 2: Substitute the given values: Area = (1/2) × 16 × 12. Step 3: Calculate: Area = (1/2) × 192 = 96 cm². Therefore, answer is B.

Question 2

A triangle has a base of 24 cm and a height of 15 cm. If the base is increased by 25% and the height is decreased by 20%, what is the percentage change in the area of the triangle?

Accepted Answer

Step 1: Original area = (1/2) × base × height = (1/2) × 24 × 15 = 180 cm². Step 2: New base = 24 + (25% of 24) = 24 + 6 = 30 cm. Step 3: New height = 15 − (20% of 15) = 15 − 3 = 12 cm. Step 4: New area = (1/2) × 30 × 12 = 180 cm². Step 5: Percentage change = [(180 − 180) / 180] × 100 = 0%. Therefore, answer is C.

Question 3

A triangle has sides of length 13 cm, 14 cm, and 15 cm. A perpendicular is drawn from the vertex opposite the 14 cm side to that side, meeting it at point P. Find the length of this perpendicular (in cm).

Accepted Answer

Step 1: Use Heron's formula to find the area of the triangle. Semi-perimeter s = (13 + 14 + 15) ÷ 2 = 21 cm. Step 2: Area = √[s(s−a)(s−b)(s−c)] = √[21 × 8 × 7 × 6] = √7056 = 84 cm². Step 3: The perpendicular from the opposite vertex to the 14 cm side acts as the height when 14 cm is the base. Using Area = (1/2) × base × height: 84 = (1/2) × 14 × h. Step 4: h = (84 × 2) ÷ 14 = 168 ÷ 14 = 12 cm. Therefore, answer is B.

RRB Group D Triangles — Area & Properties

Triangles — Area & Properties— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Triangles — Area & Properties — Practice Questions

60-Second Revision — Triangles — Area & Properties