Answer to Question #133095 in Trigonometry for joseph se

Question

What is the area of the circumscribing circle if the side of a right angle triangle are 3,4, and 5 meter?

Answer 1

Explanations & Calculations

• Circumscribed circle is a one drawn though all the vertices of a polygon.
• The aim is to find the radius of the circle so that it's possible to calculate its area (A).
• One should know that, it's a special occasion when it comes to a right triangle for which the circumscribing circle to be drawn and the hypotenuse of the triangle becomes the diameter of the circle hence the radius is the half of it.
• Therefore,

$\qquad\qquad \begin{aligned} \small A &= \small \pi r^2\\ &= \small \pi \times \Big(\frac{5}{2}\Big)^2\\ &= \small \bold{19.635\,m^2} \end{aligned}$