# Spectrum Math Grade 6 Chapter 6 Lesson 7 Answer Key Surface Area: Pyramids

Go through the Spectrum Math Grade 6 Answer Key Chapter 6 Lesson 6.7 Surface Area: Pyramids and get the proper assistance needed during your homework.

## Spectrum Math Grade 6 Chapter 6 Lesson 6.7 Surface Area: Pyramids Answers Key

The surface area of a solid is the sum of the areas of all surfaces of the solid. The surface area of a square pyramid is the sum of the area of the square base and each of the 4 triangular sides.

Each triangle’s area is $$\frac{1}{2}$$ base × height. In a pyramid, base refers to the side length and height refers to the slant height, or length. So surface area or SA = (side × side) + 4($$\frac{1}{2}$$ side × length).
SA = s2 + 2sl SA is given in square units, or units2.
If s = 6 cm and l = 10 cm, what is the surface area?

SA = s2 + 2sl
SA = 62 + 2 × 6 × 10 = 36 + 120 = 156 cm2

Find the surface area of each square pyramid.

Question 1.
a.

SA = _____ in.2
Given that side length is 8 in. and the slant height is 11 in.
The surface area for the given pyramid = s2 + 2sl
Where s=8 in. and l=11 in.
= 8×8 + 2×8×11
= 64 + 176
= 240
Thus, the surface area of the given pyramid will be 240 sq.in

b.

SA = _____ cm2
Given that side length is 15 cm and the slant height is 10.5 cm
The surface area for the given pyramid = s2 + 2sl
Where s=15 cm and l=10.5 cm
= 15×15 + 2×15×10.5
= 225 + 315
= 540
Thus, the surface area of the given pyramid will be 540 sq.cm

c.

SA = _____ m2
Given that side length is 7 m and the slant height is 12 m
The surface area for the given pyramid = s2 + 2sl
Where s=7 m and l=12 m
= 7×7 + 2×7×12
= 49 + 168
= 217
Thus, the surface area of the given pyramid will be 217 sq.m

Question 2.
a.

SA = _____ ft2
Given that side length is 9 ft and the slant height is 21 ft
The surface area for the given pyramid = s2 + 2sl
Where s=9 ft and l=21 ft
= 9×9 + 2×9×21
= 81 + 378
= 459
Thus, the surface area of the given pyramid will be 459 sq.ft

b.

SA = _____ cm2
Given that side length is 10 cm and the slant height is 8 cm
The surface area for the given pyramid = s2 + 2sl
Where s=10 cm and l=8 cm
= 10×10 + 2×10×8
= 100 + 160
= 360
Thus, the surface area of the given pyramid will be 360 sq.cm

c.

SA = _____ in.2