Find the area of figures that are combinations of polygons

To find the area of an irregular shape, break up the shape into familiar polygons. Find the area of each polygon and then add the results

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QUESTION OF

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Views #: 256

Questions #: 18

Time: 20 minutes

Pass Score: 80.0%

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Step

List

Mode

Exam

Practice

Area of an L-shaped room

1 pts

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Find the area of the L-shaped floor plan shown.

48 m²

56 m²

60 m²

72 m²

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Correct Answer

Explanation

Composite polygon made of two rectangles

1 pts

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The figure is made of two rectangles sharing a side.

What is the total area of the figure?

104 m²

120 m²

112 m²

128 m²

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Correct Answer

Explanation

Choosing all correct areas of a composite figure

1 pts

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The figure is made of a rectangle and a right triangle.

What is the total area of the figure?

72 m²

84 m²

96 m²

108 m²

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Explanation

Multiple correct expressions for area

1 pts

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The composite figure consists of a 9 cm by 4 cm rectangle and a 4 cm by 4 cm square attached to its right side.

Select all expressions that correctly represent the total area.

9×4 + 4×4

4(9 + 4)

9×8

4×13

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Explanation

Missing side in a composite polygon

1 pts

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The L-shaped figure is formed from two rectangles. The total height is 9 m and the lower vertical part is 4 m. The top horizontal side is 11 m and the lower horizontal side is 5 m.

Find the area of the figure.

64 m²

72 m²

76 m²

84 m²

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Explanation

Drag and drop: Decomposing a composite figure

1 pts

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Describe how to decompose the figure into simpler shapes.

Complete the sentence: "The figure can be split into (1) and (2)."

Please drag and drop the selected option in the right place or type it instead

two rectangles

a rectangle and a triangle

a square and a rectangle

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Explanation

Sort the steps to find area

1 pts

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Please drag and drop the options to sort them

To find the area of a composite figure made of two rectangles, sort the steps in the correct order.

Add the areas of the two rectangles.

Find the area of the first rectangle.

Find the area of the second rectangle.

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Explanation

Formula for area of a composite figure

1 pts

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The figure is composed of a rectangle of width \( w \) and height \( h \), and a right triangle with base \( b \) and height \( h \) attached to its side.

Enter a formula for the total area in terms of \( w, h, b \).

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Explanation

Matching composite figures with area expressions

1 pts

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To complete the line match

Click on an item in the first group
Click on an item in the second group
To delete a match, double click on a line

Descriptions

Rectangle (length 7) with a 3×4 rectangle attached

Rectangle (length 10) with a 5×2 rectangle removed

Expressions

7×4 + 3×4

10×5 − 5×2

Match each composite figure description with its correct area expression.

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Explanation

Classify area formulas

1 pts

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options

×\(A = bh\)

×\(A = \tfrac12 bh\)

×\(A = lw\)

Rectangle

Triangle

Classify each formula as belonging to a rectangle or a triangle.

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Explanation

What is the total area of the garden

1 pts

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A garden is shaped like an L and can be split into two rectangles. The first rectangle has an area of 24 square meters and the second has an area of 16 square meters. What is the total area of the garden?

Answer = (1)

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Explanation

Area of a composite figure with a missing dimension

1 pts

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The composite figure is shown.

The total height is 10 cm and the lower vertical part is 6 cm. The top horizontal side is 14 cm. Find the area of the figure.

80 cm²

84 cm²

88 cm²

92 cm²

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Explanation

Composite figure with a cut-out

1 pts

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A 12 m by 8 m rectangular floor has a 4 m by 3 m rectangular closet cut out from one corner.

What is the area of the remaining floor?

72 cm²

84 cm²

90 cm²

96 cm²

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Explanation

Multiple answers: Equivalent total areas

1 pts

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A composite figure is made of a 6 cm by 5 cm rectangle and a 5 cm by 4 cm rectangle attached along a 5 cm side.

6×5 + 5×4

5(6 + 4)

6×9

10×5 − 5×1

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Explanation

Drag/Drop inplace: Fill in the area statement

1 pts

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A composite figure is made of a 7 m by 3 m rectangle and a 3 m by 2 m rectangle attached on the right.

Complete the statement:

"The total area is (1) + (2) = (3) \( m^2 \)."

Please drag and drop the selected option in the right place or type it instead

7×3

3×2

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Explanation

Sort: From description to area

1 pts

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Please drag and drop the options to sort them

Sort the steps to find the area of an L-shaped figure.

Draw a line to split the figure into rectangles.

Find the area of each rectangle.

Add the areas of the rectangles.

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Explanation

Formula: Area of a step-shaped figure

1 pts

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A step-shaped figure is made of two rectangles: one of width \( a \) and height \( b \), and one of width \( c \) and height \( d \). Enter a formula for the total area.

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Correct Answer

Explanation

Match: Composite figure and decomposition

1 pts

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To complete the line match

Click on an item in the first group
Click on an item in the second group
To delete a match, double click on a line

Figures

L-shaped hallway

Rectangular patio with a triangular flower bed attached

Decompositions

Two rectangles

One rectangle and one right triangle

Match each composite figure description with a correct decomposition.

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Correct Answer

Explanation

Year 9

Area of an L-shaped room

Correct Answer

Explanation

Composite polygon made of two rectangles

Correct Answer

Explanation

Choosing all correct areas of a composite figure

Correct Answer

Explanation

Multiple correct expressions for area

Correct Answer

Explanation

Missing side in a composite polygon

Correct Answer

Explanation

Drag and drop: Decomposing a composite figure

Correct Answer

Explanation

Sort the steps to find area

Correct Answer

Explanation

Formula for area of a composite figure

Correct Answer

Explanation

Matching composite figures with area expressions

Descriptions

Expressions

Correct Answer

Explanation

Classify area formulas

Correct Answer

Explanation

What is the total area of the garden

Correct Answer

Explanation

Area of a composite figure with a missing dimension

Correct Answer

Explanation

Composite figure with a cut-out

Correct Answer

Explanation

Multiple answers: Equivalent total areas

Correct Answer

Explanation

Drag/Drop inplace: Fill in the area statement

Correct Answer

Explanation

Sort: From description to area

Correct Answer

Explanation

Formula: Area of a step-shaped figure

Correct Answer

Explanation

Match: Composite figure and decomposition

Figures

Decompositions

Correct Answer

Explanation

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