IM 1: Unit 4A Test Review
Name ___________________________
1) What are the three qualities necessary for a shape to be considered a polygon?
a)
b)
c)
2) Calculate the angle sum and measure of each angle of a regular 18-sided polygon. Show calculations.
Angle Sum =
Measure of each Angle =
3) For the shape drawn below, decide it there is reflection and/or rotational symmetry, and then complete the
corresponding questions.
Rotational Symmetry? (Y or N)
Order of Rotation:
Angles of Rotation:
Reflection Symmetry? (Y or N)
How many reflection lines?
Draw them in the picture.
4) For each of the problems below: name the shape, and then calculate the PERIMETER and AREA. Shapes are
not necessarily drawn to scale. Make sure to show calculations and include labels on all answers.
a)
7 ft
Perimeter:
Area:
Perimeter:
Area:
Perimeter:
Area:
9 ft
15 ft
b)
30 in
18 in
10 in
25 in
14 cm
c)
6 cm
5) For the following shapes calculate the lengths of the missing sides and the measures of the missing angles
based on the properties of that shape and fill them into the diagram. The shapes are not drawn to scale.
a) Rhombus with AB = 23.4 , AC = 30, BD = 36, ∠A = 122°
BC =
CD =
BE =
∠B =
∠C =
∠EAB =
∠EBA =
∠EBC =
∠EDC =
∠EDA =
∠AEB =
∠CED =
b) Isosceles Trapezoid with AB = 15, AD = 19, CD = 28, AC = 25, AE = 10, ∠A = 110°, ∠EAB = 30°, ∠EDC = 30°
BC =
CE =
BD =
BE =
∠B =
∠C =
∠EBC =
∠EAD =
∠ECB =
∠ECD =
∠EDA =
∠EBA =
∠AEB =
∠BEC =
∠CED =
6) For the picture shown below calculate the area of the gray region. Show all calculations.
5 cm
5 cm
5 cm
20 cm
5 cm
18 cm
7) Calculate the length of the missing side, along with the perimeter and area of the triangle.
Show calculations, round all answers to the nearest hundredth, and label your answers.
12 m
16 m
Side Length
Perimeter
Area
8) The diagonals of a rhombus are perpendicular and they bisect each other. The rhombus below has diagonals
of 28 cm and 44 cm. Calculate the side length, perimeter, and area.
Side Length
Area of the small Triangle
Perimeter of Rhombus
Area of Rhombus
Setup an equation to help you solve each problem. Show all of your work. You may need to use more than one
formula. Round your answers to the nearest hundredth if necessary. Label answers.
9) A square has an area = 342.25 m2. Write an equation for the area of the square and solve algebraically for
the base. Then calculate the perimeter and length of the diagonal.
base =
Perimeter =
Diagonal =
10) A rectangle has base = 3.8 cm and Perimeter = 28.6 cm. Write an equation for the perimeter of the
rectangle and solve algebraically for the height. Then calculate the area and length of the diagonal.
height =
Area =
Diagonal =
11) The isosceles triangle shown below has a base of 14 cm and a height of 17 cm. Then calculate the lengths of
the other two sides of the triangle, along with the area and perimeter of the isosceles triangle.
17cm
length =
Area =
14cm
Perimeter =
12) The circle shown below has an Area = 706.85 cm2. Write an equation for the area and solve algebraically.
Then calculate the lengths of the diameter, along with the circumference of the circle.
radius =
diameter =
Circumference =
13) Use the points
(
A = −6, −1
)
( )
B = 4, 3
( )
C = 6, −2
(
D = −4, −6
a) Plot the 4 points on the graph and label each point.
b) Connect the points in alphabetical order to form a quadrilateral.
c) Calculate the slope of each segment and diagonal.
AB
BC
CD
DA
AC
BD
d) Are the opposite sides parallel? How do you know?
e) Are the adjacent sides perpendicular? How do you know?
f) Are the diagonals perpendicular? How do you know?
g) What shape is this?
)
to answer the questions below.