Maths Topic 23 - Area and perimeter (regular shapes and compound shapes)


Area and Perimeter (regular shapes and compound/complex shapes) and the surface area of cuboids are commonly tested in 11+ and Selective School exams in the UK.

Examples

Example Question 1:

What is the area and perimeter of this shape?

Answer: area = 168cm², perimeter = 76cm

Explanation: The area of the complete rectangle, including the missing section at the bottom = 20 × 12cm = 240cm². Subtract from that the area of the rectangle that is not part of the shape 12 × 6cm = 72cm²

Area: 240 – 72 = 168cm²

Perimeter: Add all of the lengths together to find the perimeter 20 + 12 + 12 + 4 + 4 + 6 + 6 + 12 = 76cm

Example Question 2:

What is the area of this triangle? 

Answer: 24cm²

Explanation: The area of this triangle is base (6cm) × height (8cm) and then halve this number = 24cm²

Example Question 3:

What is the surface area of this cuboid?

Answer: 114cm²

Explanation: Add together the areas of all sides

Top & bottom are both 8 × 3 cm = 24cm² = 48cm² for both

Front and back are both 8 × 3 cm = 24cm² = 48cm² for both

Sides are both 3 × 3cm = 9cm² = 18cm² for both

48cm² + 48cm² + 18cm² = 114cm²

Video Tutorials

Area of Compound Shapes

 

Perimeter – Compound Shapes

 

Surface Area of a Cube

 

Triangles & Area