Step by step
The question
Question: find the surface area of a square pyramid with base 4 cm and slant height 3 cm.
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, 4 by 4.
Its area is side times side: 4 × 4.
4 times 4 is 16.
So the base is 16 cm².
3 The four triangles
Each triangle has base 4 cm.
Its height is the slant height, 3 cm: 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 × 4 × 3.
4 times 3 is 12.
Half of 12 means 12 divided by 2.
That is 6.
So one triangle is 6 cm².
There are 4 of them: 4 times 6 is 24.
4 Add all the faces
Add the base and the triangles: 16 + 24.
16 plus 24 is 40.
So the surface area is 40 cm².
Let's look back.
First: count the faces.
Then: the base.
Then: the four triangles.
Last: add all the faces.