POLYGONS ANSWER KEY

1. Find the area.

a. 32.5 sq. unitsb. 400 sq. unitsc. 500 sq. units d. 600 sq. units

Solution: Area: ½ base x height base=40 Height= 25

A= ½ 40x 25= 500 sq. unit

2. Find the area of the green rectangle. a. 30 sq. unitsb. 60 sq. unitsc. 144 sq. unitsd. 156 sq. units

Solution: Area: ½ base x height

Base= 12Use Pythagorean Theorem to get height

a= √ (169) - √144a=√ 25a= 5

A= b.h= 12x 5 = 60 sq. units

3. Find the area of trapezoid a. 63 sq. unitsb. 180 sq. unitsc. 360 sq. unitsd. 1120 sq. units

Solution: Height= 10; base= 8+28=36

A= ½ height x sum of the bases A=360/2= 180 sq. unitsA= ½ 10 x 36

4. How many square yards of each fabric (to the nearest hundredth of a yard) will she actually be using if the diameter of the cloth is 6 feet

Solution:

Diameter= 6 ftRadius= 3 ftArea of a semi circle= one half of a circle.

A= ½ (3.14) (1)*(1)= 1.57 sq. yds

5. Find the area of parallelogram ABCD. a. 504  sq. unitsb. 672  sq. unitsc. 768  sq. unitsd. 822  sq. units

Solution: A= bx h Base= 21Height=24A= 21x 24=504 sq. units

6. Find the area of the dark blue sector shown at the left.  The radius of the circle is 4 units and the length of the arc (the curved edge of the sector) measures 7.85 units.  Express answer to the nearest tenth of a square unit.

a. 0.3 sq.units b. 15.7 sq.units c. 19.7 sq.units d. 50.3 sq.units 

Solution:

A=7.85 x 3.14 x 16 2 x 3.14 x 4= 15.7 sq. units

7. Butch, the dog, is leashed to the corner of the house when he is outdoors alone. The leash is 20 feet long. Find the amount of ground area available to Butch when leashed outdoors. (Assume the corner of the house to be a right angle and the dimensions of the house to exceed 20 feet.

a.  251.3 sq.ft b. 314.2 sq.ftc.  628.3 sq.ft.

d. 942 sq.ft.

Solution:

Since the corner of the house is a right angle;

One fourth 90/360 of butch circle is blocked by the house

¾ of the area is available to butch. Therefore; =.75

A= 90/360= .25 x 3= .75e. .75 x 3.14 x 400= 942 sq.ft.

8. Find the area of this figure. Express the answer to the nearest tenth of a square inch.

a. 356.5 sq.in

b. 457.1 sq.in

c. 658.1 sq.in 

d. 1060.2 sq.in

Solution:

Find the area of the Square: A= 16x 16= 256 sq.in

Find the area of a circle: ½ 3.14 x 8x8= 100.48

A= 256+ 100.5= 356.5

9. Find the area of this figure.

a. 56.5 sq.cm

b. 140.5 sq.cm

c. 310.2 sq.cm

d. 478.2 sq.cm

Solution:

Find the area of the triangle:

½ bh= ½ 12(14)=84

Find the area of semi circle:

½ (3.14) 6*6= 56.52 or 56.5

A= 84 + 56.5 = 140.5 sq. cm

10. The side of a regular hexagon measures 12.5 feet.  What is the perimeter of the hexagon?

a. 62.5 ft 

b. 75 ft

c. 125 ft

d. 130.5 ft 

Solution:Regular means all of the sides are the same lengthHexagon= 6 sidesP= distance around the sideP= 12.5 x 6 = 75 ft

11. The diameter of this circular placemat is 15 inches.  Find the circumference to the nearest tenth of an inch.

a. 22.5 in.

b. 47.1 in.

c. 94.2 in.

d. 176.6 in.

Solution: Since r is half of diameter= r= 7.5

= 3.14 x 56.25= 176.6 in

12. Find the perimeter.

a.  68 cm

b. 76 sq. cm

c. 96 cm

d. 101 cm

Solution: Use Pythagorean Theorem to find the hypotenuse of a triangle. c= √256 + √144= √400= 20

Height = 20-16= 4 cm

Base= 24 cm

A= 4cm x 16 cm= 96 cm

13.

a. 40 sq. units

b. 32 sq. units

c. 16 sq. units

d.  8 sq. units

14. Find the area of ABCD

a. 24 sq. units

b. 32 sq. units

c. 32 sq. units

d. 64 sq. units

15. Find the area of DEF

a.  42 sq. units

b. 27 sq. units

c. 15 sq. units

d. 9 sq. units