Area between two shapes
Key Notes :
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 triangle:
area = 1/2 . base . height
Learn with an example
What is the area of the shaded region?
Write your answer as a whole number or a decimal rounded to the nearest hundredth.
_______ square meters
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 triangle.
base: 8 m
height: 12 m
Use these numbers in the formula.
inner area = 1/2 . base . height
= 1/2 . 8 . 12
= 48
Now find the units. The lengths are measured in meters, so the area is measured in square meters.
The area of the inner triangle is 48 square meters.
Next, find the area of the outer shape.
Find the base and height of the outer triangle.
base: 13 m
height: 17 m
Use these numbers in the formula.
outer area = 1/2 base . height
= 1/2 . 13 . 17
= 110.5
As with the inner triangle, the lengths of the outer triangle are measured in meters. So, the area is measured in square meters.
The area of the outer triangle is 110.5 square meters.
Finally, subtract the inner area from the outer area to find the area of the shaded region.
shaded area = 110.5 – 48
= 62.5
The area of the shaded region is 62.5 square meters.
What is the area of the shaded region?
_____ square centimeters
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: 10 cm
Use this number in the formula.
inner area=side
side = 10 . 10
=100
Now find the units. The lengths are measured in centimeters, so the area is measured in square centimeters.
The area of the inner square is 100 square centimeters.
Next, find the area of the outer shape.
Find the side length of the outer square.
side: 19 cm
Use this number in the formula.
outer area=side . side
=19 . 19
=361
As with the inner square, the lengths of the outer square are measured in centimeters. So, the area is measured in square centimeters.
The area of the outer square is 361 square centimeters.
Finally, subtract the inner area from the outer area to find the area of the shaded region.
shaded area = 361 – 100
= 261
The area of the shaded region is 261 square centimeters.
What is the area of the shaded region?
______ square meters
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: 6 m
Use this number in the formula.
inner area = side . side
= 6 . 6
= 36
Now find the units. The lengths are measured in meters, so the area is measured in square meters.
The area of the inner square is 36 square meters.
Next, find the area of the outer shape.
Find the side length of the outer square.
side: 17 m
Use this number in the formula.
outer area=side . side
= 17 . 17
= 289
As with the inner square, the lengths of the outer square are measured in meters. So, the area is measured in square meters.
The area of the outer square is 289 square meters.
Finally, subtract the inner area from the outer area to find the area of the shaded region.
shaded area = 289 – 36
= 253
The area of the shaded region is 253 square meters.
let’s practice!🖊️
