Shape and Space – Area of Compound Shapes

Compound Shapes – A shape made up of two or more simple ones

1. Split the compound shape into simple shapes
2. Find the area of each shape and add them together

Example: 

Q) Find the area of this compound shape

1. By drawing a line, we can separate the compound shape into a rectangle and a square
2. The length of the square is given by 15 – 2 = 13cm all the sides in a square are equal, so area of the square is 13 x 13 = 169 cm2

. The width of the square is 13, so the width of the rectangle is 13 + 5 = 18 and area of rectangle 18 x 2 = 36 cm2

. Sum of areas are: 36 + 169 = 205cm2

A) 205cm²

Tiles needed to cover an Area: 

1. Find the total area of the shape
2. Divide the area of the shape by the area of the tiles to show how many are needed

Example: 

Each tile is square shape with a length of 10mm.

Q) How many tiles will be needed to cover the area

1. The compound shape can be split into a square and rectangle

. Area of square: 10 – 3 = 7 → 7 x 7 = 49cm² and area of rectangle: 7 + 5 = 12 → 12 x 3 = 36cm²

. Total area 49 + 36 = 85cm²

2. Area of tile: 10 x 10 = 100mm2 → 0.01 cm2

         . 49 ÷ 0.01 = 4900

A) 4900 tiles