Areas of parallelograms, triangles and trapeziums · Usually met around P5
Areas of polygons
Cut up and add, or fill in and subtract.
How to do it
Method
Cut up and add, or fill in and subtract
L shape: 12 × 10 − 4 × 3 = 108
Another way
Cut it up
12 × 7 + 8 × 3 = 108
In full
A polygon has no single formula: turn it into shapes you know. Way 1 (cut it up): cut along helpful lines into rectangles, triangles or trapeziums, find each area and add. Way 2 (fill it in): complete it to a big rectangle and take away the part you added. An L shape can be cut across, cut down, or filled in: all three give the same answer. Work out missing sides from the ones given first: the big rectangle's length minus the top piece is the gap.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
What is the area of the polygon in the picture?
Show the answer and working
Answer: 178 cm²
Fill it in to a 14 × 15 rectangle, then take off the corner (14 − 10) × (15 − 7): 178.
Example 2
What is the area of the polygon in the picture?
Show the answer and working
Answer: 84 cm²
Cut into a rectangle and a triangle: 12 × 6 + 12 × 2 ÷ 2 = 84.
Example 3
Which working finds the area of the polygon in the picture?
- A. 18 × 4 + 14 × 6
- B. 18 × 6 − 14 × 4
- C. 18 × 6
- D. 18 × 6 − 4 × 2
Choose the right answer
Show the answer and working
Answer: D. 18 × 6 − 4 × 2
The corner is 18 − 14 = 4 by 6 − 4 = 2; the big rectangle less the corner: 18 × 6 − 4 × 2.
Practise it in the game →Areas of parallelograms, triangles and trapeziums · Free to start, unlimited questions, no download