Question 969781: How do I calculate the area of a triangle inscribed in a square that has sides equal to 7units. It is an equilateral triangle.
Also how can I calculate the area of a circle inside a square with the sides 7units also.
What would the ratio be of area of triangle:area of circle
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! This is difficult to show in words, but if you draw a triangle in a square, one of the sides of the triangle, the base, is a side of a square.
The other two sides go from the ends of the base to the middle of the top of the square.
The area of the triangle is (1/2) bh. Base is 7 units. So is the height, because the triangle goes to the top of the square.
So the area is (1/2)*7*7 or (49/2) units
For the circle in a square, draw it out. The diameter of the circle crosses the square and is 7 units.
Half the diameter is the radius or (7/2) units.
The area of the circle is pi*r^2 or (49 pi/4) units. This is an acceptable answer. The other acceptable answer is 38.48 units.
The area of the square is 7*7 or 49 units.
The ratio is 38.48 to 49
That means the circle's area is also 0.785 or 78.5% of the area of the square. It is pi/4.
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