**Area of compound figures :**

You can find the areas of polygons by breaking the polygons into smaller shapes. Then we can apply area formulas you already know.

Let us see an example problems to understand this method

**Example 1 :**

Find the area of the given polygon

**Solution :**

By drawing a horizontal line (FG) parallel to the side DC, we have divided the given polygon into two rectangles.

(i) ABFG is a rectangle

(ii) EGDC is also a rectangle

Area of ABFG :

Area of rectangle = Length x width

length (AF) = 8 ft and width AB = 5 ft

= 8 x 5 = 40 square feet ---(1)

Area of EGDC :

length (DC) = 7 ft and width DE = 3 ft

= 7 x 3 = 21 square feet ---(2)

(1) + (2)

Area of given polygon

= Area of rectangle ABFG + Area of rectangle EGDC

= 40 + 21 = 61 square feet

**Example 2 :**

Find the area of the given polygon

**Solution :**

By drawing a horizontal line (DE) parallel to the side GF, we have divided the given polygon into two rectangles.

(i) ABCE is a rectangle

(ii) DEGF is also a rectangle

Area of rectangle ABCE :

Area of rectangle = Length x width

length (AC) = 20 yd and width AB = 15 yd

= 20 x 15 = 300 square yd ---(1)

Area of DEGF :

length (DG) = 13 yd and width GF = 11 yd

= 13 x 11 = 143 square yd ---(2)

(1) + (2)

Area of given polygon

= Area of rectangle ABCE + Area of rectangle DEGF

= 300 + 143 = 443 square yd

**Example 3 :**

**Find the area of the given polygon**

**Solution : **

By drawing a horizontal line, we have divided the given shape as two parts.

(1) BECF is a rectangle

(2) ABD is triangle

Area of the given polygon

= Area of rectangle BECF + Area of triangle ABD

Area of rectangle BECF :

length CF = 16 cm and width BC = 7 cm

= length x width

= 16 x 7

= 112 cm² ----(1)

Area of triangle ABD :

Base BD = BE - DE => 16 - 8 => 8 cm

Height AB = AC - BC => 13 - 7 => 6

Area of triangle ABD = (1/2) x b x h

= (1/2) x 8 x 6 ==> 24 cm²----(2)

(1) + (2)

Area of the given polygon = 112 + 24 ==> 136 cm²

**Example 4 :**

Find the area of the given polygon

**Solution : **

By drawing a horizontal line, we have divided the given shape as two rectangles.

(1) ABCD is a rectangle

(2) CEFG is rectangle

Area of the given polygon

= Area of rectangle ABCD + Area of triangle DEFG

Area of rectangle ABCD :

length AB = 20 ft and

width AC = AG - CG => 60- 30 = 30 ft

= length x width

= 20 x 30

= 600 ft² ----(1)

Area of triangle DEFG :

length GF = 60 ft and

width FE = 30 ft

= length x width

= 60 x 30

= 1800 ft² ----(1)

(1) + (2)

Area of the given polygon = 600 + 1800 ==> 2400 ft²

**Example 5 :**

Find the area of the given polygon

**Solution :**

Extend the top edge and the right edge of the polygon.

By subtracting the area of triangle BFB from the rectangle ABCD. We can find the area of the given polygon.

Area of the given polygon

= Area of rectangle ABCD - Area of triangle GFB

Area of rectangle ABCD :

length AD = 36 inches and

width AB = 18 inches

= length x width

= 36 x 18

= 648 in² ----(1)

Area of triangle GFB :

base FG = 9 inches and

Height FB = AB - AF ==> 36 - 18 ==> 18 inches

= (1/2) x base x height

= (1/2) x 9 x 18

= 81 in² ----(1)

Area of the given polygon = 648 - 81 = 567 in²

- 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

After having gone through the stuff given above, we hope that the students would have understood "Area of compound figures".

Apart from the stuff given above, if you want to know more about "Area of compound figures, please click here

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

Widget 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**

**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**