Spectrum Math Grade 7 Chapter 5 Posttest Answer Key

This handy Spectrum Math Grade 7 Answer Key Chapter 5 Posttest provides detailed answers for the workbook questions

Spectrum Math Grade 7 Chapter 5 Posttest Answers Key

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Geometry

Find the area of each figure.

Question 1.
a.

_____ square meters.
Answer:
6 square meters.

Explanation:
Area of a Triangle = (1/2) [ Base x Height]
A = (1/2) 3 x 4
A = 3 x 2
A = 6 sq m

b.

_____ square meters
Answer:
12 square meters.

Explanation:
Area of a rectangle = Length x Width
A = 2 x 6
A = 12 sq ft.

c.

_____ square meters
Answer:
75 square meters.

Explanation:
Area of a square of side 10 m.
A1 = side  x side
A1 = 10 x 10
A1 = 100 sq m.
Area of a square of side 5 m.
A1 = side  x side
A1 = 5 x 5
A1 = 25 sq cm.
Area of a given figure is A = A1 – A2
A = 100 – 25
A = 75 square meters.

Find the area and circumference of each circle. Use 3.14 for π. Round to the nearest hundredth.

Question 2.
a.

A = ____square meters
C = ____ meters
Answer:
A = 530.66 square meters.
C = 81.64 meters.

Explanation:
Given,
Diameter = 26 m.
We know that,
π = 3.14 or 22/7
Radius = d/2
r = 26/2
r = 13 m.
A = π × r²
A = 3.14 x 13 x 13
A = 530.66 square meters.
Circumference = π × d or 2πr.
C = 2 × π × r.
C = 3.14 x 26
C = 81.64 meters.

b.

A = ____square centimeters
C = ____ centimeters
Answer:
A = 254.34 square meters.
C = 56.52 meters.

Explanation:
Given,
Radius = 9 cm.
Diameter = 2r
D = 9 x 2 = 18 cm.
We know that,
π = 3.14 or 22/7
A = π × r²
A = 3.14 x 9 x 9
A = 254.34 square meters.
Circumference = π × d or 2πr
C = 3.14 x 26
C = 56.52 meters.

c.

A = ____ square feet
C = ___ feet
Answer:
A = 38.47 square meters.
C = 21.98 meters.

Explanation:
Given,
Radius = 3.5 ft.
Diameter = 2r
D = 3.5 x 3.5 = 7 ft.
We know that,
π = 3.14 or 22/7
A = π × r²
A = 3.14 x 3.5 x 3.5
A = 38.47 square meters.
Circumference = π × d or 2πr
C = 3.14 x 7
C = 21.98 meters.

Find the length of the missing side for the pair of similar triangles.

Question 3.

Answer:
Missing side of triangle is 10.

Explanation:

\(\frac{AB}{A’B’}\) = \(\frac{AC}{A’C’}\)
\(\frac{8}{16}\) = \(\frac{AC}{20}\) Use a proportion.
16 x AC = 20 X 8
AC = \(\frac{20 × 8}{16}\)
AC = \(\frac{20}{2}\)
AC = 10
Write ratios to determine if the sides are proportional. Then, write similar or not similar.

Question 4.

_______
Answer:
similar.

Explanation:

Two triangles are similar if their corresponding angles are congruent and the lengths of their corresponding sides are proportional.
These triangles are similar as all the sides are proportional to each other.
\(\frac{K M}{K^{\prime} M^{\prime}}\) = \(\frac{2}{6}\) = \(\frac{1}{3}\)
\(\frac{K L}{K^{\prime} L^{\prime}}\) = \(\frac{2}{6}\) = \(\frac{1}{3}\)
\(\frac{M L}{M^{\prime} L^{\prime}}\) = \(\frac{2}{6}\) = \(\frac{1}{3}\)
Therefore, the angle measures are congruent.

Use the angle and side lengths given to create a triangle. Label the measurements on your drawing.

Question 5.
angle: 85°
sides: 2 inches and 4 inches.
Answer:

Explanation:
Draw a triangle that has sides of 2 inch and a non-included angle of 85°.
Step 1:   Draw a line of any length.
Step 2: Use a protractor to draw a 2-inch line that creates the desired angle with the first line (85°).
Step 3: Use a compass set at 4 inches to find where the third line will intersect the base.
Step 4: Label the triangle ABC with angle at A.

Will the following measurements make a triangle? Circle yes or no.

Question 6.
7 centimeters, 5 centimeters, 14 centimeters
yes no
Answer:

Explanation:
Given a = 7, b = 5, c = 14
a + b > c
a + c > b
b + c > a
7 + 5 is not greater then 14
5 + 14 greater then 7
Because the measurements do not follow the rules, the side lengths can not make a triangle.

Use the figure to the right to complete the following.

Question 7.
Which two lines are parallel? _____
Answer:
WX and Y Z are parallel.

Explanation:
Parallel lines are coplanar lines and never intersect.
In the above given figure, WX and Y Z are parallel lines.

Question 8.
If ∠11 is 70°, what is the measure of ∠10? ___________
Answer:
110°

Explanation:
Straight line is with 180° ,
at a point ∠10 is 180° – ∠11
∠10 = 180° – ∠11
∠10 = 180° –  70°
∠10 = 110°

Find the volume of each solid figure. Round answers to the nearest hundredth.

Question 9.
a.

V = ____ cm³
Answer:
V = 300 cm³

Explanation:
V = \(\frac{1}{3}\)s²h
Given,
s = 10 cm, h = 9 cm
V = \(\frac{1}{3}\) 10² × 9
V = \(\frac{900}{3}\)
V = 300 cm³

b.

V = ____ m³
Answer:
V = 420 m³

Explanation:
V = l × w × h.
l = 8 m, w = 10.5 m, and h = 5 m,
V = 8 × 10.5 × 5
V = 180 x 13
V = 420 m³

c.

V = ____ in.³
Answer:
V = 3,200 in³

Explanation:
V = \(\frac{1}{3}\)s2h
Given,
s = 20 in, l = 26 in
According to the Pythagorean Theorem to find the height,
a = \(\frac{1}{2}\) of the side length,
a = \(\frac{1}{2}\) x 20
a = \(\frac{20}{2}\) = 10 in,
b = the height of the pyramid, c = length (26 in)
a² + b² = c²
10² + b² = 26²
100 + b² = 676
b² = 676 – 100
b² = 576
b = 24 in
V = \(\frac{1}{3}\) 20² × 24
V = \(\frac{9,600}{3}\)
V = 3,200 in³

Name the shape that is created by the cross section.

Question 10.
a.

___________
Answer:
Triangle.

Explanation:
We know that,
A cross section of a 3-dimensional figure is the place where a plane cuts through the figure. The shape and size of the cross section depends on where the plane slices the figure.
When the plane intersects a square pyramid at a 90° angle to the base, a triangle is created.

b.

__________
Answer:
Rectangle.

Explanation:
We know that,
A cross section of a 3-dimensional figure is the place where a plane cuts through the figure. The shape and size of the cross section depends on where the plane slices the figure.
When the plane intersects a rectangular prism at a right angle, another rectangle is created.

Solve the problem.

Question 11.
A rectangular parcel of land 121 yards long and 200 yards wide is for sale. A prospective buyer wants to know the area of the parcel of land. What is the area of this property?
The area of this property is _____ square yards.
Answer:
24,200 square yards.

Explanation:
A rectangular parcel of land 121 yards long and 200 yards wide is for sale.
Area of the rectangle = l x w
Given that,
l = 121 yd, w = 200 yd.
A = 121 x 200
A = 24,200 square yards.