USING AREA TO SOLVE PROBLEMS
We may need the area of different figures to solve many real-world problems.
In this section, we are going to see, how area of figures can be used to solve real world problems.
Example 1 :
A banquet room is being carpeted. A floor plan of the room is shown below. Each unit represents 1 yard. The carpet costs $23.50 per square yard. How much will it cost to carpet the room ?
Solution :
Step 1 :
Separate the composite figure into simpler shapes as shown by the dashed lines : a parallelogram, a rectangle, and a triangle.
Step 2 :
Find the area the parallelogram.
Base (b) = 4 yards
Height (h) = 2 yards
Use the formula.
A = bh
A = 4 · 2
A = 8 square yd
The area of the parallelogram is 8 square yards.
Step 3 :
Find the area the rectangle.
Length (l) = 6 yards
Width (w) = 4 yards
Use the formula.
A = lw
A = 6 · 4
A = 24 square yd
The area of the rectangle is 24 square yards.
Step 3 :
Find the area the triangle.
Base (b) = 1 yard
Height (h) = 2 yards
Use the formula.
A = (1/2) bh
A = (1/2)(1)(2)
A = 1 square yd
The area of the triangle is 1 square yard.
Step 4 :
Find the area of the composite figure.
A = 8 + 24 + 1 = 33 square yards
Step 4 :
Calculate the cost to carpet the room.
Total cost = Area · Cost per yard
Total cost = 33 · $23.50
Total cost = $775.50
So, the cost to carpet the banquet room is $775.50.
Example 2 :
A window is being replaced with tinted glass. The plan at the right shows the design of the window. Each unit length represents 1 foot. The glass costs $28 per square foot. How much will it cost to replace the glass? Use 3.14 for π.
Solution :
Solution :
Step 1 :
Separate the composite figure into simpler shapes as shown by the dashed lines : a rectangle, two semicircles with equal area (one is one the left side of the rectangle and other one is on the right side).
Step 2 :
Find the area the rectangle.
Length (l) = 5 ft
Width (w) = 4 ft
Use the formula.
A = lw
A = 5 · 4
A = 20 square ft
The area of the rectangle is 24 square feet.
Step 3 :
Find the combined area of two semi-circles.
Radius = 2 ft
Use the formula.
A = 2 x (1/2)πr2
A = πr2
A = (3.14)(2)2
A = (3.14)(4)
A = 12.56 square ft
The combined area of two semi circles is about 12.56 square ft.
Step 4 :
Find the area of the composite figure.
A = 20 + 12.56 = 32.56 square ft
Step 5 :
Calculate the cost of tinted glass for the window.
Total cost = Area · Cost per feet
Total cost = 32.56 · $28
Total cost = $911.68
So, the cost of tinted glass for the window is $911.68.
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