3.5.3 Problems Solving with Areas
To find the area of a compound shape
You first need to break it down into simpler shapes whose areas you can calculate using the appropriate formulas.
Add up the areas of all the simple shapes to get the total area of the compound shape.
Here’s an example of how to find the area of a compound shape:
Worked example:
Find the area of the shape.
Divide the shape in two identical shapes.
These are two rectangles.
Now find area of both rectangles by using
\( A=l\times w \)
\( A \)1\( =6×2=12 \)
\( A \)2\( =8×3=24 \)
Add both areas
\( Area of shape=12+24 \)
\( =36 \)
So, area of the given shape is \( 36 cm^2 \)
Test yourself
Question 1:
Find the area of triangle \( ABC \).
[2]
Question 2:
The area of triangle \( ABC \) is \( 27 cm^2 \) and \( AB=6 cm \).
Calculate the value of \( h \).
[2]
Question 3:
A rectangle measures \( 8.5 cm \) by \( 10.7 cm \), both correct to \( 1 \) decimal place.
Calculate the upper bound of the perimeter of the rectangle.
[3]
Question 4:
The area of a square is \( 42.5 cm^2 \), correct to the nearest \( 0.5 cm^2 \).
Calculate the lower bound of the length of the side of the square.
[2]
Question 5:
\( ABDF \) is a parallelogram and \( BCDE \) is a straight line.
\( AF=12 cm \), \( AB=9 cm \), angle \( CFD=40° \) and angle \( FDE=80° \).
Calculate the height, \( h \), of the parallelogram.
[2]
Calculate the area of the trapezium \( ABCF \).
[3]