Question

a rectangle is surrounded by two sets of congruent trapeziums as shown in the adjacent figure.find the area covered by each of these trapeziums.​

Answer 1

Answer:

24.05 cm^2 & 6.93 cm^2 are areas of individual trapezium and 61.96 cm^2 is total area covered by trapeziums.

If we need to get area covered by all trapezium then Area = 20.6 × 4.6 - 16.4 × 2

= 94.76 - 32.8

= 61.96 cm^2

Now we have to find the area of trapezium one by one,

Sizes if two trapeziums are

16.4 & 20.6 cm parallel side & (4.6 - 2) / 2 = 1.3 cm height

2 cm & 4.6 cm parallel side & (20.6 - 16.4) / 2 = 2.1 cm height

Area = (1/2)(16.4 + 20.6) × 1.3 = 24.05 cm^2

Area covered by both = 2 × 24.05 = 48.1 cm^2

Area = (1/2)(2 + 4.6) × 2.1 = 6.93 cm^2

Area covered by both = 2 × 6.93 = 13.86 cm^2

Total area covered = 48.1 + 13.86 = 61.96 cm^2

Hope it helped you...

Thank you !!!