A triangular pyramid is built on a triangular concrete base of sides 10 m, 10 m, 12 m. If the height of the pyramid is 6 m, what is the volume?
Show answer & explanation
Correct answer: A
Explanation
Given:
Sides of the base triangle = 10 m, 10 m, 12 m
Height of the pyramid = 6 m
By the formula:
Area of the triangle = √(s(s − a)(s − b)(s − c))
Volume of the pyramid = (1/3) × base area × height
s = (10 + 10 + 12) / 2 = 16
Area = √(16(16 − 10)(16 − 10)(16 − 12))
= √(16 × 6 × 6 × 4)
= √2304
= 48 m²
Volume = (1/3) × 48 × 6 = 96 m³