Area List

What is the area of a circle that circumscribes a 45-45-90 triangle if the legs measure 8 cm?

What is the area of a circle inscribed within an isosceles right triangle whose legs measure 8cm?

What is the area of the square that can be placed within a 45-45-90 triangle whose legs measure 8cm? Two of the legs rest on the legs of the triangle and one of the other vertices touches the hypotenuse of the triangle?

1.If that triangle is inside the circle…There is a rule like…

If the angle subtended by a chord is 90 degrees then the triangle is said to be in a semicircle…So…The hypotenuse of the triangle will give U the diameter of the circle…

So…D^2 = 8^2 + 8^2
D^2 = 128
So…
r^2 = 128/4 [d = 1/2r so d^2 = 1/2r^2]

Use this to find the area of the circle…

Pi r^2 = Pi * 128/4

= Pi * 32
= 3.14*32
= 100.48 sqcm

2.There is a formula for radius of the circle…Like this in here
http://www.efunda.com/math/areas/CircleInscribeTriangleGen.cfm

Well…Area of the triangle = 1/2 * b * h here the legs are 8 cm…So area =

1/2 * 8 * 8 = 32 sqcm

k = 1/2(a + b + c)
k = 1/2(11.31 + 8 +
= 27.31 / 2 = 13.665 cm

Use that formula here…

32 / 13 . 665 = 2.34 sqcm…..

3.If the legs of the right triangle have lengths a and b the side of the square has length ab/(a+b)

Use that here…8 * 8/(8 + = 64 / 16 = 4cm…

Area = a^2 = 4^2 = 16 sqcm

I hope it helped U [: