**Area of Triangles and Quadrilaterals Worksheet :**

Worksheet given in this section will be much useful for the students who would like to practice problems on area of triangles and quadrilaterals.

Before look at the worksheet, if you would like to know the stuff related to area of triangles and quadrilaterals,

**Problem 1 : **

Find the area of the figure ABCD shown below.

**Solution : **

**Method 1 :**

Use AB as the base. Then, b = 16 and h = 9.

Area of the figure ABCD is

= b ⋅ h

= 16 ⋅ 9

= 144 square units

**Method 2 :**

Use AD as the base. Then, b = 12 and h = 12.

Area of the figure ABCD is

= b ⋅ h

= 12 ⋅ 12

= 144 square units

Notice that we get the same area with either base.

**Problem 2 : **

Find the height of a triangle that has an area of 12 square units and base length is 6 units.

**Solution : **

Because we want to find height of the triangle, we have to rewrite the area formula such that h is alone on one side of the equation.

Formula to find area of a triangle :

A = 1/2 ⋅ b ⋅ h

Multiply both sides by 2.

2A = b ⋅ h

Divide both sides by b.

2A / b = h

**Given :** A = 12 and b = 6.

Then, we have

(2 ⋅ 12) / 6 = h

4 = h

Hence, the height of the triangle is 4 units.

**Problem 3 : **

A triangle has an area of 52 square feet and a base of 13 feet. Are all triangles with these dimensions congruent.

**Solution : **

Because we want to find height of the triangle, we have to rewrite the area formula such that h is alone on one side of the equation.

Using formula from Problem 2, the height of the triangle is

h = (2 ⋅ 52) / 13

h = 8 feet

There area many triangles with these dimensions. Some are shown below.

**Problem 4 : **

Find the area of trapezoid WXYZ shown below.

**Solution : **

The height of the trapezoid WXYZ above is

h = 5 - 1

h = 4 units

Find the lengths of the bases :

b b b |
b b b |

Formula to find area of a trapezoid :

A = 1/2 ⋅ h ⋅ (b_{1} + b_{2})

Substitute h = 4, b_{1} = 3 and b_{2} = 7.

A = 1/2 ⋅ 4 ⋅ (3 + 7)

A = 20

Hence, the area of trapezoid WXYZ is 20 square units.

**Problem 5 : **

Find the area of the rhombus ABCD shown below.

**Solution :**

Let d_{1} and d_{2} represent lengths of the diagonals AC and BD respectively.

d_{1 } = AC = 20 + 20 = 40 units

d_{1 } = BD = 15 + 15 = 30 units

Formula to find area of a rhombus :

A = 1/2 ⋅ d_{1} ⋅ d_{2}

Substitute d_{1} = 40 and d_{2} = 30.

A = 1/2 ⋅ 30 ⋅ 40

A = 600

Hence, the area of rhombus ABCD is 600 square units.

**Problem 6 : **

Find the area of roof of the house shown below.

**Solution : **

G, H and K are trapezoids and J is a triangle. The hidden back and left sides of the roof are the same as the front and right sides.

Area of J = 1/2 ⋅ 20 ⋅ 9 = 90 ft^{2}

Area of G = 1/2 ⋅ 15 ⋅ (20 + 30) = 375 ft^{2}

Area of H = 1/2 ⋅ 15 ⋅ (42 + 50) = 690 ft^{2}

Area of K = 1/2 ⋅ 12 ⋅ (30 + 42) = 432 ft^{2}

The roof has two congruent faces of each type.

So, the total area is

= 2(90 + 375 + 690 + 432)

= 2(1587)

= 3174

Hence, the total area of the roof is 3174 square feet.

After having gone through the stuff given above, we hope that the students would have understood how to solve problems on area of triangles and quadrilaterals.

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