Solving area equations :
Here we are going to see how to use equations to solve problems about area of rectangles, parallelograms, trapezoids, and triangles?
Steps involved :
Example 1 :
After winning the state tournament, the wrestling team hangs a pennant shaped like a triangle on the gym wall. The base of the triangle is 1.5 feet long. It has an area of 2.25 square feet. What is the height of the triangle?
Base of the triangle (b) = 1.5 feet
Area of the triangle = 2.25 square feet ---(1)
Area of the triangle = (1/2) x b x h ---(2)
By equating the 1st and 2nd equations we get,
(1/2) x b x h = 2.25
(1/2) x 1.5 x h = 2.25
Multiply by 2 on both sides
1.5 x h = 2.25 x 2
by dividing 1.5 on both sides we get,
h = (2.25 x 2) / 1.5
h = 3 feet
Example 2 :
Renee is sewing a quilt whose pattern contains right triangles. Each quilt piece is a right triangle with a height of 6 inches, and an area of 24 square inches. How long is the base of each quilt piece?
Each quilt piece is in the shape right triangles.
Height of quilt piece = 6 inches
Area of each quilt piece = 24 square inches ---(1)
Area of right triangle = (1/2) x b x h ---(2)
(1) = (2)
(1/2) x b x 6 = 24
b x 3 = 24
To find the value of b, we need to divide it by 3 on both sides
b = 24/3
b = 8 inches
Example 3 :
A parallelogram shaped field in a park needs sod. The parallelogram has a base of 21.5 meters and a height of 18 meters. The sod is sold in pallets of 50 square meters. How many pallets of sod are needed to fill the field?
Base of parallelogram = 21.5 meters
Height of parallelogram = 18 ft
Area of the field = base x height
= 21.5 x 18
= 387 square meters
The sod is sold in pallets of 50 square meters.
Number of pallets to fill the field = 387/50
Hence 8 pallets are needed to fill the field.
Example 4 :
Taylor wants to paint his rectangular deck that is 42 feet long and 28 feet wide. A gallon of paint covers about 350 square feet. How many gallons of paint will Taylor need to cover the entire deck?
length of rectangular deck = 42 feet
width of rectangular deck = 28 feet
Area of rectangular deck = length x width
= 42 x 28
= 1176 square feet
A gallon of paint covers about 350 square feet.
number of gallons of paint will Taylor need to cover the entire deck = 1176 / 350
= 3.36 approximately 4
Hence, Taylor will need 4 gallons of paint to cover the entire deck.
Let us see the next example on "Solving area equations"
Example 5 :
A triangular bandana has an area of 70 square inches. The height of the triangle is 8 inches. Write and solve an equation to find the length of the base of the triangle.
Area of the triangular bandana = 70 square feet ---(1)
height of the triangle = 8 inches
Area of triangle = (1/2) x b x h ---(2)
(1) = (2)
(1/2) x b x 8 = 70
b x 4 = 80
To find the value of b, we have to divide 4 on both sides
b = 80/4
b = 20 feet
After having gone through the stuff given above, we hope that the students would have understood "Solving area equations".
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