Question

A glasshouse is in the shape of a square pyramid. Calculate the area of the four triangle faces to be nearest square metre if the side of the square is 20m and the height of the pyramid is 17m.
Pls show full working out.

Answer 1

Answer:

  789 m²

Step-by-step explanation:

Consider the cross section created by a vertical plane through the apex of the pyramid and bisecting opposite sides. The cross section is an isosceles triangle with base 20 m and height 17 m. One side of this triangle is the slant height of the face of the pyramid.

The side of the triangle above can be found using the Pythagorean theorem. A median from the apex of the triangle will divide it into two right triangles, each with a base of 10 m and a height of 17 m. Then the hypotenuse is ...

  s² = (10 m)² +(17 m)² = 389 m²

  s = √389 m ≈ 19.723 m . . . . . slant height of one triangular face

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The area of one triangular face is ...

  A = (1/2)sb

where s is the slant height above, and b is the 20 m base of the face of the pyramid. There are 4 of these faces, so the total area is ...

  total lateral area = 4A = 4(1/2)sb = 2sb = 2(19.723 m)(20 m)

  total lateral area ≈ 789 m²