Surface area of square pyramid base 6 slant height 5

Step by step

The question

Question: find the surface area of a square pyramid with base 6 and slant height 5.

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, 6 by 6.

Its area is side times side: 6 × 6.

6 times 6 is 36.

So the base is 36 square units.

3 The four triangles

Each triangle has base 6.

Its height is the slant height, 5: 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 × 6 × 5.

6 times 5 is 30.

Half of 30 means 30 divided by 2.

That is 15.

So one triangle is 15 square units.

There are 4 of them: 4 times 15 is 60.

4 Add all the faces

Add the base and the triangles: 36 + 60.

36 plus 60 is 96.

So the surface area is 96 square units.

Let's look back.

First: count the faces.

Then: the base.

Then: the four triangles.

Last: add all the faces.