**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.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**