3.3 Surface Area of Composite Shapes

​3.3 Surface Area of Composite Shapes

By Colby Yacey

​Review: 2-D area Formulas

Areas where shapes overlap or are connected together and not exposed to the surface of the object. They need to be subtracted from the total surface area

​

Areas of Overlap

Multiple Choice

What is the overlap of a composite shape?

• The 2D shapes that are a part of the 3D shapes and touch both shapes

• The 3D shapes that involved in the composite shape

• The volume of the figure

• The top of the 3D shape

Multiple Choice

Calculate the composite surface area of the figure.

• 80 cm²
• 72 cm²
• 52 cm²
• 42 cm²

Fill in the Blank

Find the surface area.

Multiple Choice

The prism is made of two cubes. What is its total surface area? (remove areas of overlap)

• 744 in²

• 816 in²

• 780 in²

• 600 in²

Multiple Choice

What is the total surface area?

• 384 cm²

• 2000 cm²

• 2384 cm²

• 2168 cm²

Multiple Choice

A garden shed is shaped like a right prism. The shed has one 7 ft-by-6 ft rectangular door and two 3 ft-by-1 1/2 ft rectangular windows. The outer walls will be painted, but not the roof, door, or windows. What is the total surface area to be painted? (remove doors, roof and windows from SA)

• 95 ft²

• 190 ft²

• 446 ft²

• 395 ft²

Multiple Choice

What is the surface area of the composite solid? remove overlap

• 216 m2

• 248 m2

• 256 m2

• 224 m2

Fill in the Blank

There are ___ overlaps in the following picture

(Remember to double)

Multiple Choice

If you were to create a composite object from two shapes that have the same area, the Total Surface Area would double!

• True

• False

Multiple Choice

Calculate the composite surface area of the figure, to the nearest square centimeter. Use 3.14.

• 4,227 cm²

• 4,542 cm²

• 4,605 cm²

• 5,262 cm²

Fill in the Blank

A baker put together the cake shown. The last step is to put frosting on the cake. How much frosting will the baker need? Round to the nearest hundredth.

Multiple Choice

Surface area is...

• The area of all sides of a three-dimensional shape added together.

• The amount of space inside a 3-dimensional shape.

• The area of a two-dimensional shape.

• The area of just the top and bottom of a three-dimensional shape.

Multiple Choice

A wedding cake is made by placing one cylindrical cake on top of another. Determine how much surface area needs to be covered with icing.

• $$440cm^2$$

• $$500cm^2$$

• $$553cm^2$$

• $$585cm^2$$

Multiple Choice

A child's building block is constructed from two triangular prisms and one rectangular prism. Calculate the total surface area of the toy.

• $$298cm^2$$

• $$352cm^2$$

• $$382cm^2$$

• $$424cm^2$$

Multiple Choice

To determine the area of overlap between these two prisms, which two values would you multiply together?

• 6 cm x 4 cm

• 7 cm x 4 cm

• 4 cm x 12 cm

• 12 cm x 6 cm

Multiple Choice

Calculate the surface area of this object to the nearest tenth.

• 410.5 mm^2
• 171.8 mm^2

• 284.9 mm^2

• 460.8 mm^2

Multiple Choice

CHALLENGE:

Calculate the surface area.

6cm is the diameter of the cylinder.

Remove areas of overlap

• 4200.4 cm²

• 4000.1 cm²

• 3860.4 cm²

• 3200.16 cm²

Multiple Choice

CHALLENGE:

All faces of a bench except the two faces that rest on the ground will be coated with a water-resistant paint. The bench is a right prism. What is the total area to be coated with the paint?

• 3731 in²

• 1160 in²

• 4487 in²

• 5243 in²

Multiple Choice

CHALLENGE:

Four identical triangular prisms are arranged together to form one large, triangular prism, as shown below. The five exterior surfaces of the large prism are then painted.

To the nearest square centimetre, what is the total area of the painted surfaces?

• 1939 cm^2

• 1. 2016 cm^2

• 1. 2 659 cm^2

• 1. 2 736 cm^2

Multiple Choice

CHALLENGE:

Ignacio makes a display shelf from 4 wooden boards. All angles formed by the boards are right angles. Ignacio plans to stain all faces of the shelf, except the back face, which will be against the wall. What is the total area Ignacio will stain?

• 780 in²

• 702 in²

• 390 in²

• 554 in²