Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Area of a Trapezium - basic geometry.
Test Yourself 1 - Solutions.


 

Remember to say to yourself for each calculation:

The area of a trapezium is
half the sum of the parallel sides
times the distance between them.

 

1.

Area = half the sum of the parallel sides

(18 + 23) ÷ 2

times the distance between them:

× 7

= 143.5 cm2

NOTE: we did not need the 8 cm - that was just included to trick someone.
 

2.
Area = half the sum of the parallel sides

(18 + 12) ÷ 2

times the distance between them:

× 10

= 150 m2

NOTE: we did not need the 11 m.
  3.

Note: we did not use the side marked 17.
 

4.

Area = half the sum of the parallel sides

(18 + 10) ÷ 2

times the distance between them:

× 16

= 224 cm2

  5.

(i) Grey trapezium:
Area = (20 + 15) ÷ 2 × 12 = 210 m2.

(ii) Green trapezium:
Area = (15 + 17) ÷ 2 × 8 = 128

(iii) Total area = 210 + 128 = 338 m2.
  6.

(i) Grey trapezium:
Area = (400 + 600) ÷ 2 × 200 = 100,000 m2.

(ii) Green trapezium:
Area = (600 + 300) ÷ 2 × 200 = 90,000 m2.

(iii) Total area = 100,000 + 90,000

= 190,000 ÷ 1,000,000 = 0.19 km2.

Remember 1,000 m = 1 km so
1,000 m × 1,000 m = 1,000,000 m2 = 1 km2.

Hence 190,000 m2 ÷ 1,000,000 = 0.19 km2.

ALTERNATIVELY - change the metres to km before calculating:

For the grey trapezium:
Area = (0.4 + 0.6) ÷ 2 × 0.2 = 0.1 km2.

Total area = 0.10 + 0.09 = 0.19 km2.
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