In this section, you will learn how to find perimeter and area of a rectangle.
A rectangle is a four-sided closed figure where the lengths of opposite sides will be equal and each vertex angle will be right angle or 90^{o }as shown below.
Let l be the length and w be the width of a rectangle.
Then, the formula for perimeter of the rectangle :
Perimeter = 2(l + w)
To get the area of any rectangle, we have to multiply its length and width.
Let l be the length and w be the width of a rectangle.
Then, the formula for area of the rectangle :
Area = l ⋅ w
Example 1 :
Find the perimeter of the figure shown below.
Solution :
The figure shown above is a rectangle with 7 inches length and 11 inches width.
Formula for perimeter of a rectangle :
= 2(l + w)^{ }
Substitute 7 for l and 11 for w.
= 2(7 + 11)
= 2(18)
= 36
So, the perimeter of the rectangle is 36 inches.
Example 2 :
The perimeter of a rectangle is 42 cm. If its width is 3 more than twice its length, then find its length and with.
Solution :
Let x be the length of the rectangle.
Then, the width is (2x + 3)
Perimeter of the rectangle = 42 cm
2(l + w) = 42
Divide each side by 2.
l + w = 21
Substitute x for l and (2x + 3) for w.
x + (2x + 3) = 21
x + 2x + 3 = 21
3x + 3 = 21
Subtract 3 from each side.
3x = 18
Divide each side by 3.
x = 6
Therefore, the length is 6 cm.
And the width is
2x + 3 = 2(6) + 3
2x + 3 = 12 + 3
2x + 3 = 15
So, the length and width of the rectangle are 6 cm and 15 cm respectively.
Example 3 :
Find the area of the figure shown below.
Solution :
The figure shown above is a rectangle with 3 cm length and 8 cm width.
Formula for area of a rectangle :
= l ⋅ w
Substitute 3 for l and 8 for w.
= 3 ⋅ 8
= 24
So, the area of the rectangle is 24 square cm.
Example 4 :
Find the area of the figure shown below.
Solution :
The figure shown above is a rectangle with 3 cm length and the measure of one the diagonals is √13 cm.
To find the area of a rectangle, we have to know its length and width. In the figure shown above, length is given, that is 3 cm. So, find its width.
In the figure shown above, consider the right triangle ABC.
By Pythagorean Theorem, we have
AB^{2} + BC^{2} = AC^{2}
Substitute.
AB^{2} + 3^{2} = (√13)^{2}
Simplify and solve for AB.
AB^{2} + 9 = 13
Subtract 9 from each side.
AB^{2} = 4
Find positive square root on both sides.
√AB^{2} = √4
AB = 2
Therefore, the width of the rectangle is 2 cm.
Formula for area of a rectangle :
= l ⋅ w
Substitute 3 for l and 2 for w.
= 3 ⋅ 2
= 6
So, the perimeter of the rectangle is 6 square cm.
Example 5 :
The length and width of a rectangular shaped wall are 8 ft and 12 ft respectively. If the cost of painting is $8.50 per square feet, then find the total cost of painting for the wall.
Solution :
To find the total cost of painting for the wall, we have to know its area. Because the wall is rectangle shaped, we can use the formula for area of a rectangle to find the area of the wall.
Formula for area of a rectangle :
= l ⋅ w
Substitute 8 for l and 12 for w.
= 8 ⋅ 12
= 96
So, the area of the wall is 96 square ft.
The cost of painting is $8.50 per square ft.
Then, the total cost of painting for 96 square ft :
= 96 ⋅ 8.50
= 816
So, the total cost of painting the wall is $816.
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