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?

The Area of rectangle is "" and the equation of the semi circle is "".

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:

=

=

=

and,

→ The Equation of semi circle is,

by substituting the values, we get

Thus the above is the correct answers.

Learn more about Area of rectangle here:

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

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