Question

HELP! A semi circle of radius 6 is centered at the origin as shown. A rectangle has two of its vertices at (5,0) and (-5,0) and the other two vertices on the semi-circle. What is the exact area of the rectangle? What is the equation of the semi circle?

Answer 1

The Area of rectangle is "$30 \ unit^2$" and the equation of the semi circle is "$y = \sqrt{36-x^2}$".

According to the question,

The vertices of rectangle,

(5, 0) and (-5, 0)

Length,

l = 10 unit

Breadth,

b = 3 unit

Radius of semi circle,

r = 6

Centre of origin,

(0, 0)

As we know,

→ The Area of rectangle is:

= $Length\times Breadth$

= $10\times 3$

= $30 \ unit^2$

and,

→ The Equation of semi circle is,

$y = \sqrt{r^2-x^2}$

by substituting the values, we get

  $=\sqrt{(6)^2-x^2}$

  $= \sqrt{36-x^2}$

Thus the above is the correct answers.

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