Compound shapes – area and perimeter
Compound or composite shapes can be made up from two or more shapes or from a shape with a smaller piece removed.
The following prior learning is useful:
Area of compound shapes
Compound shapes are shapes that can be split into 2 or more shapes.
This compound shape is made of a rectangle with a semicircle removed.
This compound shape is made of 2 parallelograms and a trapezium.
To calculate the area of compound shapes
- Split the shape into easier shapes.
- Find any missing and necessary lengths.
- Calculate the area of each part.
- Add and/or subtract to find the required area.
Example
Calculate the area of this ice cream shop logo which is made up of an A triangle with two equal sides. This means two angles are equal. and a semicircle.
Solution:
- Split the shape into easier shapes.
- Find any missing and necessary lengths.
- Calculate the area of each part
Semicircle
radius = \(13 cm \)
Area = \(πr² ÷ 2 \)
Area =\( π × 13² ÷ 2 = 265.46 cm²\) (2 d.p.)
Triangle
base = 26 cm, height 30 cmArea = \(½ \times b \times h\)A = \(½ \times 26 \times 30 = 390cm²\)
Answer:
- Add to find the required area.
\(Total area = 265.46 + 390 = 655.46 cm²\)
Example
Alby has a pond in his garden and the rest of the garden is a grass lawn.
Calculate the area of the grass lawn
Solution:
- Split the shape into easier shapes.
- Calculate the area of each part.
\(3.8 x 2 = 7.6 m² \)
\(r = 0.6\)
\( πr² = 0.6² × π \)
\(= 1.13 m² \)
Answer:
- Subtract to find the required area.
\( Area of grass = area of garden – area of pond \)
\( = 7.6 – 1.13 \)
= 6.47 m²
Question
Calculate the shaded area in this shape.
Solution:
Diameter of outer circle = 120 mm
Radius of outer circle = 60 mm
Area of outer circle = πr² = 60² × π = 11309.73 mm²
Diameter of inner circles = 60 mm since there are two circles fitting across the outer circle
Radius of inner circles = 30 mm
Area of inner circle = πr² = 30² × π = 2827.43 mm²
Shaded area = area of outer circle – 2 x area of inner circle
Answer:
Shaded area = 11309.73 – 2 x 2827.43 = 5654.86 mm²
Perimeter of compound shapes
To calculate the perimeter of compound shapes
- Split the shape into easier shapes.
- Calculate the length of any missing and necessary lengths.
- Add the lengths of all outer edges to find the total perimeter.
Example
Calculate the perimeter of this ice cream shop logo which is made up of an isosceles triangle and a semicircle.
Solution
- Split the shape into easier shapes.
There is a semi-circle arc and two straight sides.
- Calculate the length of any missing and necessary lengths.
πd ÷ 2 = π × 26 ÷ 2= 40.84 cm
Answer:
- Add the lengths of all outer edges to find the total perimeter.
Answer
40.84 + 33 + 33 = 106.84 cm (to 2 d.p.s)
Question
Calculate the perimeter of the ticket.
Solution
- Split the shape into easier shapes.
The shape is a rectangle with a semicircle removed.
Calculate the length of any missing and necessary lengths.
Semi-circular arc length = πd ÷ 2 = π × 3 ÷ 2 = 4.7 cm (to 1 d.p.)
Total perimeter = 6.5 + 1.5 + 4.7 + 1.5 + 6.5 + 6 = 26.7 cm
Test yourself
More on M2: Geometry and measures
Find out more by working through a topic
- count4 of 4
- count1 of 4
