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
Views #: 32
Questions #: 18
Time: 20 minutes
Pass Score: 80.0%
Style
Mode

Area of an L-shaped room

1 pts
volume_mute

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

8 m5 m4 m4 m
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Correct Answer

Explanation

Composite polygon made of two rectangles

1 pts
volume_mute

The figure is made of two rectangles sharing a side.

10 cm8 cm8 cm4 cm

What is the total area of the figure?

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Correct Answer

Explanation

Choosing all correct areas of a composite figure

1 pts
volume_mute

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

12 m6 m8 m

What is the total area of the figure?

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Correct Answer

Explanation

Multiple correct expressions for area

1 pts
volume_mute

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.

9 cm4 cm4 cm

Select all expressions that correctly represent the total area.

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Correct Answer

Explanation

Missing side in a composite polygon

1 pts
volume_mute

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.

11 m5 m9 m4 m

Find the area of the figure.

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Correct Answer

Explanation

Drag and drop: Decomposing a composite figure

1 pts

Describe how to decompose the figure into simpler shapes.

10 m8 m4 m

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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Correct Answer

Explanation

Sort the steps to find area

1 pts
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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Correct Answer

Explanation

Formula for area of a composite figure

1 pts

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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Correct Answer

Explanation

Matching composite figures with area expressions

1 pts

Match each composite figure description with its correct area expression.

To complete the line match

  1. Click on an item in the first group
  2. Click on the match 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
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Correct Answer

Explanation

Classify area formulas

1 pts

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

drag and drop the selected option to the right place

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Explanation

What is the total area of the garden

1 pts

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
volume_mute

The composite figure is shown.

14 cm10 cm6 cm

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.

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Correct Answer

Explanation

Composite figure with a cut-out

1 pts
volume_mute

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

12 m8 m4 m3 m

What is the area of the remaining floor?

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Correct Answer

Explanation

Multiple answers: Equivalent total areas

1 pts
volume_mute

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.

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Correct Answer

Explanation

Drag/Drop inplace: Fill in the area statement

1 pts

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
27
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Correct Answer

Explanation

Sort: From description to area

1 pts
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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Correct Answer

Explanation

Formula: Area of a step-shaped figure

1 pts

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

Match each composite figure description with a correct decomposition.

To complete the line match

  1. Click on an item in the first group
  2. Click on the match 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
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Correct Answer

Explanation

✕
0
sin cos tan
sin-1 cos-1 tan-1 π e
xy x3 x2 ex 10x
y√x 3√x √x ln log
( ) 1/x % n!
7 8 9 + MS
4 5 6 – M+
1 2 3 × M-
0 . EXP ÷ MR
± RND C = MC
Keywords
Year 9