Dr. Fiendish

Geometry Level 2

Dr Fiendish tells his pig, Freddy, to mow the northeast side of the lawn (blue) . However , Freddy accidentally mows the southwest side (yellow) . What is the difference (in units squared) between the part Freddy has mowed and the part he should mow? Freddy’s hint: SOH CAH TOA
P.S. The top-right angle = 90 degrees. @Mahdi Raza

0 approximately 6.5896 6 3 \sqrt{3} approximately 5.3914

Jeff Giff by Jeff Giff , 13, China

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1 solution

Assuming the blue triangle to be a right-angled triangle with sides 5 , 12 , 13 5,12,13 units of length, we get the area of the blue triangle as 1 2 × 5 × 12 = 30 \frac{1}{2}\times 5\times 12=30 square units, and that of the yellow triangle as 1 2 × 13 sin ⁡ 30 ° × 13 cos ⁡ 30 ° ≈ 36.58957 \frac{1}{2}\times 13\sin 30\degree\times 13\cos 30\degree\approx 36.58957 .

So the required difference is ≈ 6.58957 \approx \boxed {6.58957} square units.

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That was my original solution :)👍

Jeff Giff - 1 year ago

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