IXL | Area between two shapes

Both circles have the same center. What is the area of the shaded region?

12 in

6 in

Write your answer as a whole number or a decimal rounded to the nearest hundredth.

square inches

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Learn with an example

question

What is the area of the shaded region?

10 yd

13 yd

7 yd

square yards

key idea

To find the area of a figure with a hole in it, subtract the area of the inner shape from the area of the outer shape.

Area of a rectangle:

area

base

height

solution

To find the area of the shaded region, subtract the area of the inner shape from the area of the outer shape. Start by finding the area of the inner shape.

Find the base and height of the inner rectangle.

base: 7 yd

height: 7 yd

Use these numbers in the formula.

inner area

base

height

Now find the units. The lengths are measured in yards, so the area is measured in square yards.

The area of the inner rectangle is 49 square yards.

Next, find the area of the outer shape.

Find the base and height of the outer rectangle.

base: 10 yd

height: 13 yd

Use these numbers in the formula.

outer area

base

height

130

As with the inner rectangle, the lengths of the outer rectangle are measured in yards. So, the area is measured in square yards.

The area of the outer rectangle is 130 square yards.

Finally, subtract the inner area from the outer area to find the area of the shaded region.

shaded area

130

–

The area of the shaded region is 81 square yards.

Looking for more? Try these:

Lesson: Area of circles

Lesson: Area of triangles

Lesson: Area of rectangles

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Teacher tools

Work it out

Not feeling ready yet? These can help:

GG.2Area of rectangles and squares

GG.6Area of triangles

BB.6Area of circles

Lesson: Area of circles

Lesson: Area of triangles

Lesson: Area of rectangles

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