About "Solving area equations"

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 :

  • First we have to draw the picture by using the given details
  • Write the formula to find the area of the given shape.
  • Substitute the given values.
  • By using the inverse operations, we can find the the unknown.

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?

Solution :

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?

Solution :

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?

Solution :

 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 

  =  7.74

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?

Solution :

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.

Solution :

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

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