Chapter 11 Test Review
Do on your own paper. Draw a diagram. All answers must be exact unless otherwise told in
the problem.
1.
A walk 2 m. wide surrounds a rectangular grass plot 30 m. long and 10 m. wide. Find
the area of the walk. [176 m2]
2.
The longer diagonal of a rhombus is 2 times as long as the shorter diagonal. Find the
length of the shorter diagonal if the area is 24 in.2 [ 2 6 in. ]
3.
A triangular shaped boat sail is 16 ft. high. Find the length of the base if the area is 640
ft.2 [80 ft.]
4.
Find the area of an equilateral triangle with a side of 24 m. [ 144 3 m2 ]
5.
Find the area of an isosceles right triangle with hypotenuse of 10 cm. [25 cm2]
6.
Find the area of the shaded region. [18 units2]
3
3
3
7.
3
Given: altitude AD of right ∆CAB. Find the area of ∆ADB. [ 75 3 units2]
8
A
30
5
B
D
C
8.
Find the area of the trapezoid whose coordinates are (–2, 0); (0, 4); (5, 4); (17, 0).
[48 units2]
9.
Find the area of the rhombus whose coordinates are (–2, –1); (3, 2); (–2, 5); (–7, 2).
[30 units2]
10.
Find the area of the trapezoid to the right.  72  60 2 units2 




10
12
45
11.
Find the area of the trapezoid to the right.
 12x 2  2x 2 3 

units2 


3



45
2x
2x
60
12.
Find the area of the rhombus to the right. 18 3 units2 


30
6
13.
A rhombus has sides of length 10 m. and one diagonal of length 16 m. Find its area.
[96 m2]
14.
Find the area of a regular hexagon with apothem 3 3 . 54 3 units2 


15.
Find the area of a regular hexagon with radius 8. 96 3 units2 


16.
If the area of a regular hexagon is 36 3 cm.2, find its apothem and the length of its
side. side  2 6 cm; apothem  3 2 cm


17.
If the apothem of a regular hexagon is 5 m., find its perimeter and area.
P  20 3 units; A  50 3 m2 


18.
An equilateral triangle and a regular hexagon are both inscribed in a circle with radius
6. Find the area of each polygon. Atriangle  27 3 units2; Ahexagon  54 3 units2 


19.
A side of a regular hexagon is s units long. Find the area of the hexagon in terms of s.

2
3s2 3
 A  2 units 


20.
A side of a regular hexagon is twice the square root of its apothem. Find the length of
the apothem and the side. Hint: put the apothem in terms of the side.
apothem  3 units; side  2 3 units


21.
The apothem of a regular pentagon is 13 cm. Find the area of the pentagon to the
nearest hundredth. [613.93 cm2]
22.
A regular hexagon and a square are circumscribed about a circle with radius 10. How
much more area does the square have than the hexagon?  400  200 3 units 2 


23.
A flower garden is to be made with a white decorative brick border as shown
by the unshaded part of this figure. The inner square planting area is formed
by connecting the midpoints of the 12 foot sides of the outer regular octagon.
Find the area of the brick border.  72  144 2 ft 2 






24.
Find the perimeter of the figure to the left. Shaded parts are semicircles.
[(30 + 8) cm]
15 cm.
8 cm.
In 25 – 27, find the circumference and area of each circle.
25.
C  6 2 cm


[A = 18 cm2]
square with side
length of 6 cm.
26.
C  4 3 cm


[A = 12 cm2]
27. [C = 12 cm]
[A = 36 cm2]
equilateral triangle
with side length of 6
cm.
regular hexagon
with side length of
6 cm.
28.
Suppose ΔABC is a right triangle with right C and CD  AB . If CD = 8, AD = 16, and
BD = 4, find the following ratios. Hint: Draw a diagram.
a.
area of ΔACD [4 : 1]
area of ΔCDB
29.
Two radii of similar regular polygons are in the ratio of 5 : 4. The sum of their perimeters is
20. Find the perimeters of each polygon. 1st perimeter =11 1 ; 2nd perimeter  8 8 
9
9

30.
The apothems of two similar polygons are in the ratio 3 : 5. If the area of the larger
polygon is 35 square units, find the area of the smaller polygon. [12.6 units2]
b.
area of ΔACD [4 : 5]
area of ΔABC