Go through the **Spectrum Math Grade 6 Answer Key**** Chapter 6 Pretest** and get the proper assistance needed during your homework.

## Spectrum Math Grade 6 Chapter 6 Pretest Answers Key

**Find the area or surface area of each figure.**

Question 1.

a.

A = ____ sq. in.

Answer:

Given triangle has base length of 60 in. and height of 8 in.

A = \(\frac{1}{2}\) × b × h

= \(\frac{1}{2}\) × 60 × 8

= \(\frac{1}{2}\) × 480

= 240

A = 240 square inches

b.

A = _____ sq. m

Answer:

Given rectangle is 75m long and 5m wide.

Area of rectangle = length×width

= 75×5

= 375 sq.m

Thus, the area will be 375 sq.m

c.

A = ____ sq. cm

Answer:

The base length of first triangle is 11 cm and height is 8 cm.

Area of first triangle = \(\frac{1}{2}\) × b × h

= \(\frac{1}{2}\) × 11 × 8

= \(\frac{1}{2}\) × 88

= 44 sq.cm

The base length of second triangle is 11 cm and height is 8 cm.

Area of second triangle = \(\frac{1}{2}\) × b × h

= \(\frac{1}{2}\) × 11 × 8

= \(\frac{1}{2}\) × 88

= 44 sq.cm

Area of third triangle with base length of 11 cm and height 6 cm will be \(\frac{1}{2}\) × b × h

= \(\frac{1}{2}\) × 11 × 6

= \(\frac{1}{2}\) × 66

= 33 sq.cm

Area of figure = (Area of first triangle)+(Area of second triangle)-(Area of third triangle)

= 44+44-33

= 88-33

= 55

Area of figure will be 55 sq.cm

Question 2.

a.

A = _____ sq. m

Answer:

Given figure has base length of 3.6 m and height of 1.7 m.

Area of parallelogram = base × height

= 3.6 × 1.7

= 6.12

Thus, the area of parallelogram will be 6.12 sq.m

b.

SA = _____ sq. m

Answer:

Given rectangular solid is 14 m wide, 20 m long and 12 m high

Surface area of the solid = 2×(length×width + width×height + height×length)

= 2×(20×14 + 14×12 + 12×20)

= 2×(280+168+240)

=2×688

=1376 sq.m

The surface area of the rectangular solid is 1376 sq.m

c.

SA = _____ sq. cm

Answer:

Given that side length is 8.5 cm and the slant height is 9.6 cm

The surface area for the given pyramid = s^{2} + 2sl

Where s=8.5 cm and l=9.6 cm

= 8.5×8.5 + 2×8.5×9.6

= 72.25 + 163.2

= 235.45

Thus, the surface area of the given pyramid will be 235.45 sq.cm

**Find the volume of each rectangular solid.**

Question 3.

a.

V = ____ cu. cm

Answer:

Given cuboid is 15 cm long, 10 cm wide and 8 cm high

Volume of cuboid = length×width×height

= 10×15×8

= 1200 cu.cm

b.

V = ____ cu. ft.

Answer:

Given cuboid is 10 ft long, 12 ft wide and 8 ft high

Volume of cuboid = length×width×height

= 10×12×8

= 960 cu.ft

c.

V = ____ cu. m

Answer:

Given cuboid is \(\frac{4}{5}\) m long, \(\frac{4}{5}\) m wide and \(\frac{1}{5}\) m high

Volume of cuboid = length×width×height

= \(\frac{4}{5}\)×\(\frac{4}{5}\)×\(\frac{1}{5}\) m

= \(\frac{16}{125}\) cu.m

**Use the coordinate grids to find the missing vertex of each polygon.**

Question 4.

a. a rectangle with points at (4, -3), (4, -6), and (-3, -6)

The missing point is at _____

Answer:

Let us assume the given points (4, -3), (4, -6), and (-3, -6) as A,B and C respectively.

Connect the vertices A,B,C and then draw lines straight from points A and C.

The intersecting point of both will be the point D.

Thus, point D will be (-3,-3)

b. a right triangle with points at (-3, 2) and (4, -5)

The missing point is at _____ or ____

Answer:

Let us assume the given points (-3, 2) and (4, -5) as A and B respectively.

If points A (-3, 2) and B (4, -5) are vertices of the hypotenuse of a right triangle.

Connect the vertices and then draw lines straight from points A and B.

The intersecting points will be the missing point.

Point C can be (4,2) or (-5,-3)

**Solve each problem.**

Question 5.

The sail on a boat is shaped like a right triangle. Its base is 15 feet and its height is 22 feet. What is the area?

The area is _____ square feet.

Answer:

Given that the boat is shaped like a right triangle with base length of 15 feet and its height of 22 feet.

Area of triangle = \(\frac{1}{2}\) × b × h

= \(\frac{1}{2}\) × 15 × 22

= \(\frac{1}{2}\) × 330

= 165

The area is 165 square feet.

Question 6.

A shoe box is 6 inches wide, 10 inches long, and 5 inches high. What is the volume?

The volume is ____ cubic inches.

Answer:

Given that a shoe box is 6 inches wide, 10 inches long, and 5 inches high.

Volume of shoe box = length×width×height

= 10×6×5

= 300

The volume of shoe box is 300 cubic inches.

Question 7.

A ski jump is shaped like a right triangle. Its base is 27 feet long and the highest point on the ramp is 4 feet. What is the area of the ski jump?

The area is ____ square feet.

Answer:

Given that a sky jump is shaped like a right triangle. Its base is 27 feet long and the height is 4 feet.

Area of triangle = \(\frac{1}{2}\) × b × h

= \(\frac{1}{2}\) × 27 × 4

= \(\frac{1}{2}\) × 108

= 54

The area is 54 square feet.