Area Of Compound Shapes

Split the compound shape into two rectangles and find the area of each rectangle:

Let us label the two rectangles A and B .

Area of Rectangle A :

We need to calculate the unknown length. To do this we need to use the measurements we are given in the question that are parallel to the unknown side:

If we add together the 3 sides, we will get the length of rectangle A .

4+5+5= 14m

\begin{aligned} \text { Area }_{A} &=\text { length } \times \text { width } \\\\ \text { Area }_{A} &=14 \times 2 \\\\ &=28 \end{aligned}

Area of Rectangle B :

We need to calculate the unknown length. To do this we need to use the measurements we are given in the question that are parallel to the unknown side:

The length of the entire compound shape is 10m . We need to subtract the 2m of shape A to get just the length of shape B .

10-2=8

\begin{aligned} \text { Area }_{B} &=\text { length } \times \text { width } \\\\ \text { Area }_{B} &=8 \times 5 \\\\ &=40 \end{aligned}

\begin{aligned} \text { Compound Area } &=\text { Area of } A+\text { Area of } B \\\\ &=28+40 \\\\ &=68 \end{aligned}

\text { Area }=68 \mathrm{~m}^{2}

Split the compound shape into three rectangles:

Let us label the two rectangles A, B and C .

Area of Rectangle A :

\begin{aligned} \text { Area }_{A} &=\text { length } \times \text { width } \\\\ \text { Area }_{A} &=12 \times 5 \\\\ &=60 \end{aligned}

Rectangle C is congruent to Rectangle A so we can just double the area of rectangle A .

60 \times 2 = 120

Area of Rectangle B :

We need to calculate the unknown width. To do this we need to use the measurements we are given in the question that are parallel to the unknown side:

The entire width of the shape is 13m . If we subtract 5m and 5m (the width of rectangles A and C ).

13-5-5=3m

\begin{aligned} \text { Area }_{B} &=\text { length } \times \text { width } \\\\ \text { Area }_{B} &=7 \times 3 \\\\ &=21 \end{aligned}

\begin{aligned} \text { Compound Area} &=\text { Area of } A+\text { Area of } B+\text { Area of } C \\\\ &=60+21+60 \\\\ &=141 \end{aligned}

\text { Area }=141 \mathrm{~m}^{2}

While this is the total area we need to calculate how many tins of paint will be needed to cover the wall. If each tin of paint covers a distance of 4 square metres, we need to divide 4 into 141 .

141 \div 4=35.25

Since you cannot buy 0.25 of a can of paint, we need to round our answer to 36 tins of paint.

Answer = 36 tins of paint will be needed

Split the compound shape into a triangle and rectangle:

*Note: This shape is a trapezium. Another way to find the area of this shape would be simply to use the formula for the area of a trapezium. For this question, because we are focusing on compound shapes, we will separate the shape into a triangle and a rectangle.

Let us label the two shapes A and B .

Area of Triangle A :

\begin{aligned} \text { Area }_{A} &=\frac{b \times h}{2} \\\\ \text { Area }_{A} &=\frac{2 \times 8}{2} \\\\ &=8 \end{aligned}

Area of Rectangle B :

We need to calculate the unknown length. To do this we need to use the measurements we are given in the question that are parallel to the unknown side:

The height of the entire compound shape is 6m . We need to subtract the 2m of shape A to get just the length of shape B .

6-2=4

\begin{aligned} \text { Area }_{B} &=\text { length } \times \text { width } \\\\ \text { Area }_{B} &=8 \times 4 \\\\ &=32 \end{aligned}

\begin{aligned} \text { Compound Area } &=\text { Area of } A+\text { Area of } B \\\\ &=8+32 \\\\ &=40 \end{aligned}

\text { Area }=40 \mathrm{~m}^{2}

Split the compound shape into two rectangles. 

Let us label the two rectangles A and B .

Area of Rectangle A:

\begin{aligned} \text { Area }_{A} &=\text { length } \times \text { width } \\\\ \text { Area }_{A} &=8 \times 2 \\\\ &=16 \end{aligned}

In this case we are not given enough information to find the area of Rectangle B. .

\begin{aligned} \text { Compound Area } &=\text { Area of } A+\text { Area of } B \\\\ 48 &=16+\text { Area of } B \\\\ \text { Area of } B &=48-16 \\\\ \text { Area of } B &=32 \end{aligned}

Now that we know the area of rectangle B, we can calculate the value of x .

\begin{aligned} \text { Area of } B &=l \times w \\\\ 32 &=l \times 4 \\\\ l &=\frac{32}{4} \\\\ l &=8 m \end{aligned}

x = 8m

Split the compound shape into a rectangle and trapezium. Once we find the area of the two shapes we can subtract the area of the triangle. 

Let us label the three shapes A , B and C .

Area of Trapezium A :

Add the parallel sides: 10+11=21

Divide by 2: 21 \div 2=10.5

Times by the height: 10.5 \times 2=21m^2

Step by step guide: Area of a trapezium (Coming soon)

Area of Rectangle B :

\begin{aligned} \text { Area }_{B} &=\text { length } \times \text { width } \\\\ \text { Area }_{B} &=11 \times 7 \\\\ &=77 \mathrm{~m}^{2} \end{aligned}

Area of Triangle C :

We need to calculate the unknown width. To do this we need to use the measurements we are given in the question that are parallel to the unknown side:

The width of the entire compound shape is 11m . We need to subtract the 5m and 4m from 11m to get the width of shape C .

11-5-4=2

\begin{aligned} \text { Area }_{C} &=\frac{1}{2}(\text { base } \times \text { height }) \\\\ \text { Area }_{C} &=\frac{2 \times 6}{2} \\\\ &=6 m^{2} \end{aligned}

\begin{aligned} \text { Compound Area } &=\text { Area of } A+\text { Area of } B-\text { Area of } C \\\\ &=21+77-6 \\\\ &=92 \end{aligned}

\text { Area }=92 \mathrm{~m}^{2}