Unit 7 Review

Triangles

100

How many triangles can be made with the side lengths 6 inches, 3 inches, and 9 inches? 

a. ambiguously defined

b. nonexistent

c. a unique triangle

d. exactly 2 triangles. 

b. nonexistent 

6 + 3 = 9

9 = 9 

The two shorter side lengths would not touch. A triangle cannot be formed. 

200

Which best describes a triangle with side lengths of 5 cm, 12 cm, and 13 cm?

a. ambiguously defined

b. nonexistent

c. a unique triangle

d. exactly two triangles

c. a unique triangle can be formed.

5 + 12 = 17

17 >13

300

Which best describes a triangle with side lengths of 3 inches, 4 inches, and 8 inches?

a. ambiguously defined

b. nonexistent

c. exactly 1 unique triangle

d. exactly 2 triangles 

b. nonexistent

3 + 4 = 7

7< 8 

The two side lengths would not touch, therefore no triangles can be formed. 

400

A triangle has an angle measure of 65º, another angle measure of 38º. The third angle measure is unknown. Find the measure of the third angle. 

The third measure must be exactly 77º.

Triangle Angle Sum theorem states that the sum of angles inside a triangle must equal 180º

180 - 65 - 38 = 77º

or

65+38 = 103

180-103= 77º

500

How many triangles can be formed with angle measures 54º, 25º, and 103º?

None. 

54+ 25+ 103 = 182

The sum of the angle measures in a triangle MUST equal 180º.

Circles

100

A circle has a diameter of 3 cm. 

What is the circumference?

9.42 cm

C=πd

C=(3)(3.14)

C=9.42

200

A circle has a radius of 10 ft. 

Find the area of the circle. 

314 ft²

A=πr²

A=(3.14)(10²)

A= 314

300

The circle has a diameter of 12 km.

Find the area of the circle. 

113.04 km²

r= 1/2(12)

r=6

A=πr²

A=(3.14)(6²)

A=113.04

400

The circumference of a circular pin is approximately 19.5 cm. What is the area?

30.18 cm²

C=πd      19.5=πd   d=6.21

r=1/2d  r= 1/2(6.21)   r=3.1

A=πr²     A=(3.14)(3.1²)

A=30.18

500

A circular fountain has sprays an area of 78.5 feet².

Find the circumference.

C=31.4 ft

A=πr²       78.5=(3.14)(r²)    25=r²          r=5

C=2πr

C=2(3.14)(5)   C=31.4 ft

Surface Area

100

Find the surface area of the rectangular prism.

(On slide 1)

136 yds²

200

Find the surface area of the rectangular prism. 

Slide 2

340 yd²

300

Find the surface area of the triangular prism

(slide 3)

576 cm²

400

Find the surface area of the cube

(cube 4)

181.5 cm²

500

Find the surface area of the triangular prism. 

Slide 5

1656 cm²

Volume

100

Find the volume of the cube.

(slide 6)

512 in³

200

Find the volume of the locker.

Slide 7

2880 in³

300

What is the height of the rectangular prism if the volume is 60 in³

3 inches

400

What is the volume of the tent?

42 feet³

500

What is the volume of the solid figure?

246 m³

Composite Figures

100

Find the area of the figure. 

Slide 11

57 cm²

200

Find the volume of the solid figure. 

Slide 12

110 m³

300

Find the volume of the solid.

Slide 13

400 m³

400

Find the volume of the solid figure. 

Slide 14

450 meters³

500

Find the area of the circle and the shaded region. 

Slide 15

11.94 yd² is the total shaded area. 

12.56 yd² is circle

24.5 yd² is total triangle

24.5-12.56 = 11.94