Surface area of square pyramid base 10 slant height 12

Step by step

The question

Question: find the surface area of a square pyramid with base 10 and slant height 12.

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, 10 by 10.

Its area is side times side: 10 × 10.

10 times 10 is 100.

So the base is 100 square units.

3 The four triangles

Each triangle has base 10.

Its height is the slant height, 12: 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 × 10 × 12.

10 times 12 is 120.

Half of 120 means 120 divided by 2.

That is 60.

So one triangle is 60 square units.

There are 4 of them: 4 times 60 is 240.

4 Add all the faces

Add the base and the triangles: 100 + 240.

100 plus 240 is 340.

So the surface area is 340 square units.

Let's look back.

First: count the faces.

Then: the base.

Then: the four triangles.

Last: add all the faces.