Shaded Area Surface Area and Volume

The area of the shaded region is 118 ft².

Which equation can be used to find the value of x, in feet?

• 15x + 8 = 118

• 15x + 32 = 118

• 15x - 24 = 118

• 15x - 16 = 118

Tags

CCSS.3.MD.C.7D

Niko plans a Japanese Zen garden in a square section of his backyard. The plans include a fountain surrounded by a moss covered region. The base of the fountain is formed by two intersecting squares with sides of equal length. The budget for the moss is $375 and the cost of the moss is $5 per square foot.

Select the true statements.

• The area of the square section of the backyard that contains the garden is 40 ft².

• The area, in square feet, of the fountain base formed by intersecting squares can be represented by 6(6) -2(2)(2).

• The area, in square feet, of the moss-covered region can be represented by 10(10) - 24.

• The cost of the moss is less than the budgeted amount.

The figure shown is composed of a right rectangular prism attached to a right triangular prism. The surface area of the figure is 130 cm². What is the value of n, in centimeters?

• 2

• 3

• 4

• 2.5

A toy maker glues 8 wooden blocks in the shape of right rectangular prisms, stacked on top of each other, into a tower. The surface of the tower is 2,400 cm². The dimensions of the completed tower are shown. What is the surface area, in square centimeters, of one of the blocks used to make the tower?

• 650

• 580

• 290

• 800

Tags

CCSS.7.G.B.6

A stop sign is shaped like an octagon, and all of the sides are the same length. The dimensions are shown in the diagram. What is the area of the stop sign, in square inches?

• 478

• 548

• 758

• 80

Tags

CCSS.6.G.A.1

The area of the shaded region is 44 cm².

Which equation can be used to find the value of x, in centimeters?

• 10x=44

• 20x=44

• 22x=44

• 16x=44

The floor plans for the rectangular dining room of a Moroccan restaurant include a decorative tile floor surrounded by carpet. The cost of the carpet is $4 per square foot. The owner budgets $5,000 to spend on carpeting.

• The total area of the rectangular dining room in square foot is the product of 40 and 24.

• An expression that represents the area of the tiled floor in square feet is 1/2(6)(12) + 16(12).

• The area of the carpeted floor is the sum of the area of the dining room and the area of the tiled floor.

• The cost of the carpet is less than the budgeted amount.

A shipping department lines boxes in a row so that the back faces of the boxes touch, as shown in the figure. Each box is in the shape of a right rectangular prism with a height of 5 in. and a length of 10 in. The width of the entire row of boxes is 48 in. Each of the boxes has a surface area of 160 in².

How many boxes are lined up in a row?

• 15

• 16

• 24

• 30

Tags

CCSS.7.G.B.6

The figure shown is composed of a right rectangular prism attached to a cube. The surface area of the figure is 152 in². What is the value of x, in inches?

• 1

• 2

• 3

• 4

Dahlia is painting the ceiling of a sunroom with dimensions as shown. The ceiling is in the shape of a hexagon with all sides the same length. What is the total area of the ceiling in square meters?

• 208

• 256

• 288

• 304

Tags

CCSS.6.G.A.1