Area and perimeter problems

The coconut farmer wants to fence his land and plant trees. He needs both perimeter and area. So do gardeners, builders, and tailors. Let's see how to handle problems that mix the two.

What is this?

Reading the problem carefully tells us which measurement is needed:

• Words like fence, boundary, border, lace, frame, edge, around → perimeter.
• Words like carpet, paint, tile, grass, garden, floor, cover → area.

Sometimes a problem asks for both. For example: "A garden is 30 m × 20 m. (a) How much wire is needed to fence it? (b) How much grass is needed to cover it?"

• (a) Perimeter = 2 × (30 + 20) = 100 m wire.
• (b) Area = 30 × 20 = 600 sq m grass.

When two shapes are joined, the perimeter or area can be found by breaking the shape into rectangles. Find each piece, then add.

If a corner is cut off from a big rectangle, area = big − small. But for perimeter, you have to walk along the outline carefully, because the cut adds new sides.

In an L-shape, you can imagine it as a big rectangle with a corner missing. The area is big rectangle minus the missing piece. The perimeter is the sum of all 6 sides of the L-shape.

Worked examples

Example 1. A rectangular room is 8 m × 5 m. Find (a) perimeter and (b) area.

• Perimeter = 2 × (8 + 5) = 26 m.
• Area = 8 × 5 = 40 sq m.

Example 2. A square garden has perimeter 60 m. What is its area?

• Each side = 60 ÷ 4 = 15 m.
• Area = 15 × 15 = 225 sq m.

Example 3. A floor is 10 m × 6 m. Tile size is 1 m × 1 m. How many tiles needed, and how much border lace?

• Tiles = 10 × 6 = 60 tiles.
• Lace (perimeter) = 2 × (10 + 6) = 32 m.

Try it

1. Find both perimeter and area for a rectangle 14 m × 9 m.
2. A square plot has each side 12 m. Find perimeter and area.
3. The perimeter of a square is 48 cm. What is its area?
4. A room 7 m × 5 m needs tiles of 1 sq m. How many tiles? How much skirting board (perimeter)?
5. The area of a rectangle is 56 sq m and its length is 8 m. Find breadth and perimeter.

Hands-on

Plot planner. Draw a small rectangle (say 6 cm × 4 cm) on grid paper. Mark the area in squares. Trace the perimeter with a coloured pencil. Note both numbers.

Floor plan. Sketch the floor plan of your room on grid paper. Measure the actual sides and use a scale (say 1 cm = 1 m). Calculate area (for the carpet) and perimeter (for the skirting).