The base of a right pyramid is an equilateral triangle with area 16√3 cm². If the area of one of its lateral faces is 30 cm², then its height (in cm) is:
Answers
Given : The base of a right pyramid is an equilateral triangle with area 16√3 cm². area of one of its lateral faces is 30 cm²
To find : height (in cm) i
Solution:
The base of a right pyramid is an equilateral triangle with area 16√3 cm²
Area of an equilateral triangle = (√3 / 4) Side ²
(√3 / 4) Side ² = 16√3
=> Side ² = 64
=> Side = 8 cm
Distance of center of triangle to mid point of Side for Equilateral triangle = side/ 2√3 = 8/ 2√3 = 4/√3
Let say Height = H
Slant Height = √((4/√3)² + H²)
Area of lateral surface = (1/2) * base * Slat Height
= (1/2) * 8 * Slant height = 30
=> Slant height = 15/2
15/2 = √((4/√3)² + H²)
=> 225/4 = 16/3 + H²
=> 611/12 = H²
=> H = 7.135 cm
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