A triangular flowerbed is being planted inside a circular area of grass. What is the area of the grass (the area surrounding the flowerbed)? (Use 3.14 for π.)

Question

mathstudent55 · Answer

Are there dimensions? Maybe a figure?

mathstudent55 · Answer

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mathstudent55 · Answer

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mathstudent55 · Answer

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treelessavy · Answer

On my computer for cyber school it doesn't show and figures. It just shows the question and the answers and thats why i'm really confused.

mathstudent55 · Answer

The area of the grass is the area of the circle minus the area of the triangular flowerbed.
The area of the circle is simply A = (pi)r^2
I am assuming the triangular flowerbed is a regular (equilateral) triangle inscribed in the circle.
The area of the triangular flowerbed is made up of the areas of 3 congruent, isosceles triangles, whose congruent sides measure r. Each isosceles triangle is made up of two congruent 30-60-90 triangles.
Each of the 6 small triangles has a base of r*sqrt(3)/2 and a height of r/2.
The area of one 30-60-90 triangle is 
A = (1/2)bh 
A = (1/2)(r*sqrt(3)/2) * (r/2)
A = (r^2 * sqrt(3) )/ 8
This is the area of only one 30-60-90 triangle. The triangular flowerbed is made up of six of these small triangles so the total area of the flowerbed is (Af = area of flowerbed)
Af = 6 * (r^2 * sqrt(3) )/ 8
Af = (3*sqrt(3)*r^2)/4
The area of the grass (Ag) is
Area of circle minus area of flowerbed, so
Ag = (pi)r^2 - (3*sqrt(3)*r^2)/4
Now plug in 3.14 for pi and simplify.

mathstudent55 · Answer

You weren't given the radius of the circle either? Also, I assumed the triangle is equilateral and inscribed in the circle. From the problem description, the case could be like the drawing below, and my assumption wiould be incorrect.

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