**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

- Area and polygons
- Inverse operations
- Area of square and rectangles
- Area of quadrilaterals
- Area of a parallelogram
- Finding the area of a trapezoid
- Finding the area of a rhombus
- Area of triangles
- Finding the area of a triangle
- Problems using area of a triangles
- Solving area equations
- Writing equations using the area of a trapezoid
- Solving multistep problems
- Area of polygons
- Finding areas of polygons
- Real world problems involving area and perimeter of polygon

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