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# Help! We've got a math problem... SM6b

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I don't normally have trouble with these sorts of things, but I just can't figure out how help my daughter to solve this with the "tools" she has. I also don't have the teacher's guide or answer key... It's SM6b Workbook Problem 4 from Unit 7, Exercise 8. It says "The figure shows an equilateral triangle and a circle. The radius of the circle is 20 ft. Find the area of the shaded part. "

The figure is a circle shown with an equilateral triangle inscribed in it. The area below the triangle is shaded and one third of the triangle is shaded. The radius is shown as 20 ft. My daughter found the area of the entire circle and wants to subtract 2/3 of the area of the triangle. And then subtract 2/3 the area that remains, but she can't figure out the area of the triangle.

The only way I can think of to solve it is to cut the triangle into 30-60-90 degree triangles and solve with 20 as the hypotenuse, but that hasn't been taught yet. The answers I see online for this type of problem all use trigonometry which also hasn't been learned yet. I wonder if we're overlooking something simple.

Ideas?

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The area below the triangle is shaded and one third of the triangle is shaded = 1/3 area of circle

ETA:

I don't have the teacher guide or workbook. I'm just picturing the problem from the way you describe.

Edited by Arcadia in CA
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The area below the triangle is shaded and one third of the triangle is shaded = 1/3 area of circle

ETA:

I don't have the teacher guide or workbook. I'm just picturing the problem from the way you describe.

That sounds right to me. If 1/3 of the triangle is shaded and 1/3 of the remaining area in outside the triangle is shaded, 1/3 of the area of the entire circle must be shaded. It seems that the answer would be (3.14)*(20^2)*(1/3).

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Yes... that would be the simple thing we were overlooking! Thank you!

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