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8. Find the surface area of a triangular pyramid if the area of each phase is 16 cm² and each of its lateral faces has an area of 9 cm².

Sagot :

Kayasiaidn

Answer:

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

Step-by-step explanation:

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