**Writing equations using the area of a trapezoid :**

Here we are going to see how to use equations to solve problems based on the shape trapezium.

**Steps involved :**

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

**Example 1 :**

A garden in the shape of a trapezoid has an area of 44.4 square meters. One base is 4.3 meters long and the other base is 10.5 meters long. The height of the trapezoid is the width of the garden. How wide is the garden?

**Solution :**

Given :

Area of trapezoid = 44.4 square meters --- (1)

base length = 10.5 m and 4 m

Formula to find area of trapezoid =

(1/2) x h (a + b) --(2)

Equating the first and second equation we get,

(1/2) x h (a + b) = 44.4

(1/2) x h (10.5 + 4) = 44.4

(1/2) x h x 14.5 = 44.4

Multiplying 2 on both sides, we get

h x 14.5 = 44.4 x 2

Dividing 14.5 on both sides, we get

h = (44.4 x 2)/14.5

h = 6.12 approximately 6 m

**Example 2 :**

The cross section of a water trough is shaped like a trapezoid. The bases of the trapezoid are 18 feet and 8 feet long. It has an area of 52 square feet.What is the height of the cross section?

**Solution :**

Given :

Area of trapezoid = 52 square feet --- (1)

base length = 18 ft and 8 ft

Formula to find area of trapezoid =

(1/2) x h (a + b) --(2)

Equating the first and second equation we get,

(1/2) x h (a + b) = 52

(1/2) x h (18 + 8) = 52

(1/2) x h x 26 = 52

Multiplying 2 on both sides, we get

h x 26 = 52 x 2

Dividing 26 on both sides, we get

h = 104/26

h = 4 feet

**Example 3 :**

The top of a desk is shaped like a trapezoid. The bases of the trapezoid are 26.5 and 30 centimeters long. The area of the desk is 791 square centimeters. The height of the trapezoid is the width of the desk. Write and solve an equation to find the width of the desk.

**Solution :**

Given :

Area of trapezoid = 791 square centimeters --- (1)

base length = 26.5 and 30 centimeters

Formula to find area of trapezoid =

(1/2) x h (a + b) --(2)

Equating the first and second equation we get,

(1/2) x h (a + b) = 791

(1/2) x h (26.5 + 30) = 791

(1/2) x h x 56.5 = 791

Multiplying 2 on both sides, we get

h x 56.5 = 791 x 2

Dividing 56.5 on both sides, we get

h = 791/56.5

h = 14 centimeter

**Example 4 :**

A section in a stained glass window is shaped like a trapezoid. The top base is 4 centimeters and the bottom base is 2.5 centimeters long. If the area of the section of glass is 3.9 square centimeters, how tall is the section?

**Solution :**

Given :

Area of trapezoid = 39 square centimeters --- (1)

base length = 4 and 2.5 centimeters

Formula to find area of trapezoid =

(1/2) x h (a + b) --(2)

Equating the first and second equation we get,

(1/2) x h (a + b) = 39

(1/2) x h (4 + 2.5) = 39

(1/2) x h x 6.5 = 39

Multiplying 2 on both sides, we get

h x 6.5 = 39 x 2

Dividing 6.5 on both sides, we get

h = 78/6.5

h = 12 centimeter

**Example 5 :**

The cross section of a metal ingot is a trapezoid. The cross section has an area of 39 square centimeters.The top base of the cross section is 12 centimeters. The length of the bottom base is 2 centimeters greater than the top base. How tall is the metal ingot? Explain

**Solution :**

Given :

Area of trapezoid = 39 square centimeters --- (1)

Length of top base = 12 centimeters

Length of bottom base = 12 + 2 = 14 centimeter

Formula to find area of trapezoid =

(1/2) x h (a + b) --(2)

Equating the first and second equation we get,

(1/2) x h (12 + 14) = 39

(1/2) x h (26) = 39

Multiplying 2 on both sides, we get

h x 26 = 39 x 2

Dividing 6.5 on both sides, we get

h = 78/26

h = 3 centimeters

- 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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