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

Find the area or surface area of each figure.

Question 1.
a. A = ____ sq. in.
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
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 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
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
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
Given that side length is 8.5 cm and the slant height is 9.6 cm
The surface area for the given pyramid = s2 + 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
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.
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
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 _____
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 ____
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.
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.
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.
Area of triangle = $$\frac{1}{2}$$ × b × h
= $$\frac{1}{2}$$ × 27 × 4
= $$\frac{1}{2}$$ × 108