Find the area enclosed by of the following figures.
Answers
Answer:
area of octagon = area of 2 trapeziums + area of rectangle
= 2(1/2 x h x sum of parallel sides) + (lxb)
= 2(1/2 x 8 x (22 + 10) + 22 x 10 (all sides are equal in the octagon)
=2(1/2 x 8 x 32) + 220
= 2(128) + 220
= 256 + 220
= 476 cm^2
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Answer: 476 cm^3
Step-by-step explanation:
Split the figure into one rectangle and two trapezoids (like shown in the figure).
Find the area of the upper trapezoid: [ (a + b) / 2 ] x h => a = top length, b = lower length, & h = height
- [ (10 + 22) / 2 ] x 8 = (32 / 2) x 8 = 32 x 4 = 128 cm^2
Find the area of the rectangle: l x b => l = length & b = breadth
- 22 x 10 = 220 cm^2
Find the area of the lower trapezoid: (Use the same formula that was used for the upper trapezoid)
- [ (10 + 22) / 2 ] x 8 = (32 / 2) x 8 = 32 x 4 = 128 cm^2
Therefore, the total area of the regular octagon is the sum of all of the broken down figures.
- 128 + 220 + 128 = 476 cm^2
Therefore, the total area of the regular octagon = 476 cm^2.