Answer Keys: Area, Surface Area & Volume

Student Concept Worksheet Answers

1

42 cm^2

Triangle: A = (1/2) x 12 x 7 = (1/2) x 84 = 42 cm^2

2

36 in^2

Parallelogram: A = 9 x 4 = 36 in^2

3

32 m^2

Trapezoid: A = (1/2)(6 + 10) x 4 = (1/2)(16) x 4 = 8 x 4 = 32 m^2

4

SA = 94 cm^2, V = 60 cm^3

SA = 2(5x4) + 2(5x3) + 2(4x3) = 2(20) + 2(15) + 2(12) = 40 + 30 + 24 = 94 cm^2
V = 5 x 4 x 3 = 60 cm^3

5

180 in^2

SA = 2(8x6) + 2(8x3) + 2(6x3) = 2(48) + 2(24) + 2(18) = 96 + 48 + 36 = 180 in^2

Practice Worksheet Answers

Part A: Area of Triangles

#	Given	Work	Answer
1	b=10, h=6	(1/2) x 10 x 6	30 cm^2
2	b=14, h=9	(1/2) x 14 x 9	63 in^2
3	b=8.5, h=4	(1/2) x 8.5 x 4	17 m^2
4	b=15, h=12	(1/2) x 15 x 12	90 ft^2

Part B: Parallelograms and Trapezoids

#	Shape	Work	Answer
5	Parallelogram	12 x 7	84 cm^2
6	Trapezoid	(1/2)(8+14) x 6 = (1/2)(22) x 6	66 in^2
7	Parallelogram	9.5 x 8	76 m^2
8	Trapezoid	(1/2)(5+11) x 4 = (1/2)(16) x 4	32 ft^2

Part C: Surface Area

9

108 cm^2

SA = 2(6x4) + 2(6x3) + 2(4x3) = 48 + 36 + 24 = 108 cm^2

10

340 in^2

SA = 2(10x5) + 2(10x8) + 2(5x8) = 100 + 160 + 80 = 340 in^2

11

294 cm^2

Cube: SA = 6 x (7 x 7) = 6 x 49 = 294 cm^2 (all 6 faces are identical squares)

Part D: Volume

12	5 x 4 x 6	120 cm^3
13	12 x 3 x 4	144 in^3
14	8 x 8 x 2	128 m^3
15	5 x 5 x 5	125 ft^3

Part E: Word Problems

16

12 m^2

Triangle sail: A = (1/2) x 4 x 6 = 12 m^2 of fabric

17

700 in^2

SA = 2(15x10) + 2(15x8) + 2(10x8) = 300 + 240 + 160 = 700 in^2

18

4,608 in^3

V = 24 x 12 x 16 = 4,608 cubic inches of water

19

32 ft^2

Trapezoid: A = (1/2)(6 + 10) x 4 = (1/2)(16) x 4 = 32 ft^2

Challenge Questions:

#20: Height = 5 cm. V = l x w x h, so 120 = 6 x 4 x h, 120 = 24h, h = 120/24 = 5 cm

#21: Box 1: 10 x 5 x 4 = 200 in^3. Box 2: 8 x 8 x 3 = 192 in^3. Box 1 has greater volume.

FAST Practice Quiz Answers

1

B) 48 cm^2

Triangle: A = (1/2) x 12 x 8 = (1/2) x 96 = 48 cm^2. Note: A (96) is the common error of forgetting to divide by 2.

2

B) 60 in^3

V = 5 x 4 x 3 = 60 in^3. Note: C has wrong units (in^2).

3

B) 32 m^2

Trapezoid: A = (1/2)(6 + 10) x 4 = (1/2)(16) x 4 = 8 x 4 = 32 m^2

4

Select: 1st, 3rd, and 4th statements

Triangle is half of rectangle - TRUE
Volume in square units - FALSE (cubic units!)
Surface area is total of all faces - TRUE
Parallelogram is base x height - TRUE
Rectangular prism has 4 faces - FALSE (has 6 faces)

5

B) 208 in^2

SA = 2(8x6) + 2(8x4) + 2(6x4) = 96 + 64 + 48 = 208 in^2

6

C) 54 ft^2

Parallelogram: A = b x h = 9 x 6 = 54 ft^2

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