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.
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?
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?
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
Area of Compound Shapes
Perimeter – Compound Shapes
Surface Area of a Cube
Triangles & Area