Splitting into rectangles

Some figures are not plain rectangles, but they can be split into rectangles. Find the area of each rectangle and add them up: that is the area of the whole figure.

One figure in the book is shaped like an arch (all measures in metres). Its outline is a rectangle 5 m wide and 3 m tall, but a gap 3 m wide and 2 m tall is cut out of the middle of its bottom edge, leaving two legs, each 1 m wide. Split it into three rectangles:

• the top strip is 5 m by 1 m, so 5 sq m;
• each leg is 1 m by 2 m, so 2 sq m.

The area is 5 + 2 + 2 = 9 sq m. (Check another way: the full outline 5 × 3 = 15 sq m, minus the gap 3 × 2 = 6 sq m, is also 9 sq m.)

Charan's house is on a rectangular plot, and its plan is split into rectangular rooms. On a plan, use the fact that opposite sides of a rectangle are equal, and add up the sides of neighbouring rooms to find a side that is not marked. The master bedroom is 15 ft by 15 ft, so its area is 225 sq ft. The small bedroom is 15 ft wide and its area is 180 sq ft, so its other side is 180 ÷ 15 = 12 ft. When you know the area and one side of a rectangle, divide to find the other side.

The Area Maze puzzles use the same idea. In puzzle (a), a big rectangle is split into four smaller rectangles by one straight line across and one straight line down.

• Top row: 13 sq cm (left) and 26 sq cm (right).
• Bottom row: 15 sq cm (left) and an unknown area (right).

The two top rectangles have the same height, and 26 is twice 13, so the right-hand column is twice as wide as the left. The bottom-right rectangle must then be twice the bottom-left one: 2 × 15 = 30 sq cm.