Surface area of square pyramid base 8 m slant height 7 m

Step by step

The question

Question: find the surface area of a square pyramid with base 8 m and slant height 7 m.

1 Count the faces

The surface area is the area of all the outside faces.

This pyramid has a square base and 4 triangles, all the same.

2 The base

The base is a square, 8 by 8.

Its area is side times side: 8 × 8.

8 times 8 is 64.

So the base is 64 m².

3 The four triangles

Each triangle has base 8 m.

Its height is the slant height, 7 m: straight up the middle of the face.

Careful: we need the slant height, up the face.

Not the height inside the pyramid.

One triangle is half of base times height: ½ × 8 × 7.

8 times 7 is 56.

Half of 56 means 56 divided by 2.

That is 28.

So one triangle is 28 m².

There are 4 of them: 4 times 28 is 112.

4 Add all the faces

Add the base and the triangles: 64 + 112.

64 plus 112 is 176.

So the surface area is 176 m².

Let's look back.

First: count the faces.

Then: the base.

Then: the four triangles.

Last: add all the faces.