IXL | Area between two shapes

What is the area of the shaded region?

30 mi

21 mi

9 mi

16 mi

square miles

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Learn with an example

question

What is the area of the shaded region?

35 yd

22 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 square:

area

side

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 side length of the inner square.

side: 22 yd

Use this number in the formula.

inner area

side

484

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

The area of the inner square is 484 square yards.

Next, find the area of the outer shape.

Find the side length of the outer square.

side: 35 yd

Use this number in the formula.

outer area

side

1,225

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

The area of the outer square is 1,225 square yards.

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

shaded area

1,225

–

484

741

The area of the shaded region is 741 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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