Question 333138: OK, I am a homeschool mom that has hit a block. I am sure that this is quite simple. Our problem is this:
The radius of a circle is pi cm. The base of a triangle is pi cm. The area of the circle equals the area of the triangle. What is the height of the triangle?
Our answer book simply gives an answer and I prefer for my student to know how to get the correct answer not just know the correct answer. Thank you for any assistance you can provide.
Found 2 solutions by nerdybill, tinbar:
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! The radius of a circle is pi cm. The base of a triangle is pi cm. The area of the circle equals the area of the triangle. What is the height of the triangle?
.
Formulas:
area of circle = (pi)r^2
area of triangle = (1/2)bh
.
But:
r (radius) = pi
and
b (base) = pi
where
pi = 3.14
.
since:
"area of circle" = "area of triangle"
(pi)r^2 = (1/2)bh
(pi)(pi)^2 = (1/2)(pi)h
Solving for h:
dividing both sides by pi:
(pi)^2 = (1/2)h
2(pi)^2 = h
2(3.14)^2 = h
19.72 cm = h
Answer by tinbar(133)  (Show Source):
You can put this solution on YOUR website! if the radius of the circle is pi, then the area is given by the formula, Area = pi*(r^2), where r is the radius. since our radius is pi, our area will be
pi*(pi^2) = pi*pi*pi = pi^3
now if our triangle contains the same area and we are given the base, then we can determine the height
area of triangle = base*height*0.5, and we know our area = pi^3
therefore pi^3 = pi*0.5*height, if we rearrange, we get height = pi^3/pi*2
and by simplifying we get height = 2*pi^2
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