Real world problems involving area and perimeter :
We can find the areas of polygons by breaking the polygons into smaller shapes. Then we can apply area formulas we already know.
Here we are going to see how to solve practical problems using the concept area and perimeter of polygons.
Example 1 :
The diagram shows the shape and dimensions of Teresa’s rose garden.
(a) Find the area of the garden
(b) Teresa wants to buy mulch for her garden. One bag of mulch covers 12 square feet. How many bags will she need?
By drawing a horizontal line, we have divided the given shape as two parts.
(1) ABCD is a rectangle
(2) CEFG is also a rectangle
Area of the garden
= Area of rectangle ABCD + Area of the rectangle CEFG
Area of rectangle ABCD :
length AB = 15 ft and width BD = 9 ft
= length x width
= 15 x 9
= 135 ft² ----(1)
Area of rectangle CEFG :
length CE = 24 ft and width CF = AF - AC ==> 18 - 9 = 9 ft
= length x width
= 24 x 9
= 216 ft² ----(1)
(1) + (2)
Area of the rose garden = 135 + 216 ==> 351 ft²
Number of bags that she needed = 351/12 ==> 29.25
Hence, she will need 30 bags of mulch
Example 2 :
The diagram shows the floor plan of a hotel lobby. Carpet costs $3 per square foot. How much will it cost to carpet the lobby?
By observing the above picture, we can find two trapeziums of same size. Since both are having same size. We can find area of one trapezium and multiply the area by 2.
Area of trapezium = (1/2) h (a + b)
h = 15.5 ft a = 30 ft and b = 42 ft
= (1/2) x 15.5 x (30 + 42)
= (1/2) x 15.5 x 72 ==> 15.5 x 36==> 558 square feet
Area of floor of a hotel lobby = 2 x 558
= 1116 square feet
Cost of carper per square feet = $3
= 3 x 1116 ==> $ 3348
Amount spent for carpet = $ 3348
Example 3 :
Jess is painting a giant arrow on a playground. Find the area of the giant arrow. If one can of paint covers 100 square feet, how many cans should Jess buy?
Now we are going to divide this into three shapes. Two triangles and one rectangle.
Area of rectangle = length x width
= 18 x 10 ==> 180 square feet
Area of one triangle = (1/2) x b x h
= (1/2) x 6 x 10 ==> 30 square feet
Area of two triangles = 2 x 30 = 60 square feet
Total area of the given shape = 180 + 60
= 240 square feet
one can of paint covers 100 square feet
Number of cans needed = 240/100 = 2.4 approximately 3.
Hence Jessy has to 3 cans of paint.
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