Lesson 8: Determine Surface Area of Pyramids6.GR.4

I can…

I can find the surface area of a pyramid by adding the base area and the lateral faces.

Key words

• Surface Area of Pyramids — The total area of a pyramid's base and triangular faces. Formula: SA = B + lateral area.
• Pyramid — A solid with a flat bottom and triangle sides that meet at one point on top.
• Slant height — The height of a side triangle, measured along its slanted face.
• Lateral face — A triangle side of a pyramid, not the bottom.
• Base — The flat bottom of a pyramid.
• Apex — The point at the top of a pyramid where the sides meet.
• Lateral area — The total area of just the side triangles, not the bottom.
• Surface area — The total area of every face of a solid, base included.

Steps

1. My square pyramid has a 6 in. × 6 in. base and a slant height of 8 in.
2. First the base area: 6 × 6 = 36.
3. Now one triangular face: ½ × 6 × 8 = 24. A square pyramid has 4 of them, so 4 × 24 = 96.
4. I add the base and the side faces: 36 + 96 = 132.
5. So the total surface area is 132 in². I used the slant height (8) for the triangles, not the pyramid's height.

Try it

A play tent is shaped like a square pyramid with a base edge of 4 ft and a slant height of 7 ft. What is the total surface area, floor included?

Check your answer

72 ft²

Base: 4 × 4 = 16 ft². Each lateral face: ½ × 4 × 7 = 14 ft². Four faces: 4 × 14 = 56 ft². SA = 16 + 56 = 72 ft². Surface area uses square units (ft²).

Sentence starter

I know ___ because ___.

Goal: I can explain my work using the words pyramid, slant height, lateral face, and base.