Question
A pyramid has an equilateral triangle as its base, of
which each side is 8 cm. Its slant edge is 24 cm. The whole surface area of the pyramid (in cm2) is:Solution
ATQ, we can say that To find the surface area of the pyramid, Find the area of the base and the area of each triangular face. The area of the equilateral triangle base is given by: A = (√3)/4) x side^2 From the data side = 8 cm A = (√3)/4) x (8 cm)^2 = 16√3 cm² To find the area of each triangular face, The height of the pyramid can be found as follows h² = slant height² - (1/2 x base)² h² = 24² - (1/2 x 8)² = 576 - 16 = 560 h = √560 = 4√35cm Now find the area of each triangular face using the A = (1/2) x base x height A = (1/2) x 8 cm x 4√35cm A = 16√35cm² Since there are four triangular faces, the total surface area of the pyramid is: Total Surface Area = Base Area + 4 x Triangle Area = 16√3 cm² + 4 x 16√35 cm² = 16√3 cm² + 4 x 16√35 cm² = 16(√3 + 4 √35) cm² Therefore,The whole surface area of the pyramid is 16(√3 + 4 √35) cm²
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