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

## Spectrum Math Grade 7 Chapter 5 Pretest Answers Key

**Check What You Know**

**Find the area of each figure.**

Question 1.

a.

____________ square yards

Answer:

6 square yards.

Explanation:

Area of a rectangle = Length x Width

A = 3 x 2 = 6

Area = 6 square yards.

b.

____________ square centimeters

Answer:

4 square centimeters.

Explanation:

Area of a Triangle = (1/2) [ Base x Height]

A = (1/2) 4 x 2

A = 2 x 2

A = 4 sq cm

c.

____________ square centimeters.

Answer:

20 square centimeters.

Explanation:

Area of a rectangle of length L = 6 cm and width 5 cm.

A1 = length x width

A1 = 6 x 5

A1 = 30 sq cm.

Area of triangle of Base 4 cm and height 5 cm.

A2 = (1/2) base x height

A2 = (1/2) x 4 x 5

A2 = 2 x 5

A2 = 10 sq cm.

Area of a given figure is A = A1 – A2

A = 30 – 10

A = 20 square centimeters.

**Find the circumference and area of each circle. Use 3.14 for π.**

Question 2.

a.

A = ____________ square meters

C = ____________ meters

Answer:

A = 200.96 square meters

C = 50.24 meters

Explanation:

Given that,

Radius = 8 m

Diameter = 2r

D = 2 x 8

D = 16 cm.

We know that,

π = 3.14 or 22/7

A = π × r^{2
}A = 3.14 x 8 x 8

A = 200.96 square meters.

Circumference = 2πr

C = 2 x 3.14 x 8

C = 50.24 meters.

b.

A = ____________ square feet

C = ____________ feet

Answer:

A = 153.86 square feet

C = 43.96 feet

Explanation:

Given,

Diameter = 14 ft

Radius = d/2

r = 14/2

r = 7 ft

We know that,

π = 3.14 or 22/7

A = π × r^{2
}A = 3.14 x 7 x 7

A = 153.86 square feet.

Circumference = 2πr

C = 2 x 3.14 x 7

C = 43.96 feet.

c.

A = ____________ square yards

C = ____________ yards

Answer:

A = 4,298.66 square yards

C = 232.36 yards

Explanation:

Given,

Radius = 37 yd

Diameter = 2r

D = 37 x 2

D = 74 yd.

We know that,

π = 3.14 or 22/7

A = π × r^{2
}A = 3.14 x 37 x 37

A = 4,298.66 square yards

Circumference = 2πr

C = 2 x 3.14 x 37

C = 232.36 yards.

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

Question 3.

Answer:

missing side length is 15.

Explanation:

\(\frac{AB}{A’B’}\) = \(\frac{BC}{B’C’}\)

\(\frac{15}{25}\) = \(\frac{9}{B’C’}\) Use a proportion.

15 × BC = 25 × 9

BC = \(\frac{25 × 9}{15}\)

BC = 5 x 3

BC = 15.

**Write ratios to determine if the sides are proportional. Then, write similar or not similar.**

Question 4.

Answer:

not similar.

Explanation:

Two parallelogram are not similar if their corresponding angles are not congruent and the lengths of their corresponding sides are not proportional.

\(\frac{AB}{LM} \) = \(\frac{5}{6} \)

\(\frac{BD}{MO} \) = \(\frac{3}{4} \)

\(\frac{DC}{ON} \)= \(\frac{5}{6} \)

\(\frac{CA}{NL} \)= \(\frac{3}{4} \)

Therefor the angle measures are not congruent.

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

Question 5.

Angles: 60° and 100°

Side: 2 inches

Answer:

Explanation:

Step 1: Use a ruler to draw a line that is 2 in.

Step 2: Use a protractor to draw a line that creates the desired angle with the first line (60°).

Step 3: Use the protractor to measure the 2^{nd} known angle 100°from the other end of your original line.

Step 4: Label the triangle.

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

Question 6.

5 meters, 9 meters, 20 meters

yes

no

Answer:

Explanation:

Given a = 5, b = 9, c = 20

a + b > c

a + c > b

b + c > a

5 + 9 is not greater then 20

9 + 20 is greater then 5

Because the measurements do not follow the rules, the side lengths can not make a triangle.

**Find the volume of each figure.**

Question 7.

a.

V = _____________ in.^{3}

Answer:

V = 588 in.^{3}

Explanation:

V = \(\frac{1}{3}\)s^{2}h

Given,

s = 14 in, h = 9 in

V = \(\frac{1}{3}\) 14^{2} × 9

V = \(\frac{1764}{3}\)

V = 588 in^{3}

b.

V = _____________ cm^{3}

Answer:

V = 400 cm.^{3}

Explanation:

V = \(\frac{1}{3}\)s2h

Given,

s = 10 cm, l = 13 cm

According to the Pythagorean Theorem to find the height,

a = \(\frac{1}{2}\) of the side length,

a = \(\frac{1}{2}\) x 10

a = \(\frac{10}{2}\) = 5 in.

b = the height of the pyramid, c = length (26 in)

a^{2} + b^{2} = c^{2}

5^{2} + b^{2} = 13^{2}

25 + b^{2} = 169

b^{2} = 169 – 25

b^{2} = 144

b = 12 in

V = \(\frac{1}{3}\) 10^{2} × 12

V = \(\frac{1200}{3}\)

V = 400 in^{3}

c.

V = _____________ in.^{3}

Answer:

V = 560 in.^{3}

Explanation:

V = l × w × h.

l = 16 in, w = 7 in and h = 5 in,

V = 16 × 7 × 5

V = 560 in^{3}^{
}

**Tell what shape is created by each cross section.**

Question 8.

Answer:

Square.

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 triangular prism square is created.

Question 9.

Answer:

Quadrilateral.

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 an angle, it will create a quadrilateral, but not necessarily a rectangle.

**Use the figure below to answer the questions.**

Question 10.

Name an angle complementary to angle

SOP. ___________

Answer:

∠POT

Explanation:

If two angles add up to 90 degrees then they are known as complementary angles.

∠POT is a complementary angle.

Question 11.

Name an angle supplementary to angle

MOQ. ____________

Answer:

∠MOP or ∠QOT

Explanation:

If two angles add up to 180 degrees then they are known as supplementary.

∠MOP or ∠QOT are supplementary angles.

**Solve each problem.**

Question 12.

A scale drawing of a car is 3 inches to 12 inches. If the car is 48 inches high, how high is the drawing?

The drawing is _______________________ inches high.

Answer:

12 inches high.

Explanation:

A scale drawing of a car is 3 inches to 12 inches.

If the car is 48 inches high.

The height of the drawing = 12 x 3 = 48 inches.

Question 13.

On a map, each inch represents 25 miles. What is the length of a highway if it is 6 inches long on a map?

The highway is _____________________ miles long.

Answer:

150 miles long.

Explanation:

On a map, each inch represents 25 miles.

If is the length of a highway is 6 inches long on a map then the highway is,

1 inch = 25 miles

6 inches = 6 x 25 = 150 miles long.

Question 14.

Adam needs to wrap a package that is 11 inches long, 8.5 inches wide, and 6 inches high. What is the volume of the package?

The package’s volume is ______________________ cubic inches.

Answer:

561 cubic inches.

Explanation:

Adam needs to wrap a package that is 11 inches long, 8.5 inches wide, and 6 inches high.

V = lbh.

The volume of the package, 11 x 8.5 x 6 = 561 cubic inches.