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 = s^{2} + 2sl SA is given in square units, or units^{2}.

If s = 6 cm and l = 10 cm, what is the surface area?

SA = s^{2} + 2sl

SA = 6^{2} + 2 × 6 × 10 = 36 + 120 = 156 cm^{2}

**Find the surface area of each square pyramid.**

Question 1.

a.

SA = _____ in.^{2}

Answer:

Given that side length is 8 in. and the slant height is 11 in.

The surface area for the given pyramid = s^{2} + 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 = _____ cm^{2}

Answer:

Given that side length is 15 cm and the slant height is 10.5 cm

The surface area for the given pyramid = s^{2} + 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 = _____ m^{2}

Answer:

Given that side length is 7 m and the slant height is 12 m

The surface area for the given pyramid = s^{2} + 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 = _____ ft^{2}

Answer:

Given that side length is 9 ft and the slant height is 21 ft

The surface area for the given pyramid = s^{2} + 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 = _____ cm^{2}

Answer:

Given that side length is 10 cm and the slant height is 8 cm

The surface area for the given pyramid = s^{2} + 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}

Answer:

Given that side length is 22 in and the slant height is 17.5 in

The surface area for the given pyramid = s^{2} + 2sl

Where s=22 in and l=17.5 in

= 22×22 + 2×22×17.5

= 484 + 770

= 1254

Thus, the surface area of the given pyramid will be 1254 sq.in