An isosceles right triangle is inscribed in a circle.

Question

An isosceles right triangle is inscribed in a circle. The hypotenuse of the triangle is the diameter of the circle. Write a function f in terms of x that represents the area of the shaded region. Leave your answer in terms of π.

Image: https://dw6y82u65ww8h.cloudfront.net/organisations/48/A2.C05.15.O1_2015113145146.png

Answer 1

Hi Peyton M.

Thanks for the link to the picture

Since you have an Isosceles Right Triangle or a 45 45 90 Triangle you can simply apply the Pythagorean Theorem to calculate the hypotenuse or longest side

a² + b² = c²

In an Isosceles Triangle, a = b

In the picture at your link that is x; so a = b = x

x² + x² = c²

Can you continue from here to solve for c the diameter of the Circle?

Since your Isosceles Right Triangle is inscribed in the circle, the area of the shaded region would be

f(x) = Area of the Circle - Area of the Inscribed Triangle

I hope this helps please send me a message if you have any questions