## Fifth Graders Workbook

Posted by trickofmind on May 3, 2010 – 3:29 am

You are given a Rectangle with a length of 20 inches.

There is a circle dead center on the rectangle, and its

diameter happens to be sqrt(50) inches.

The circle is noted to have two drawn diameters,

connecting the points at which the edge of the

rectangle and the circle intersect that are opposite of

each other. The diameters are at right angles to each other.

What is the area of the rectangle that is not covered by the circle?

– Jordan McMichael

May 3rd, 2010 at 3:40 pm

102.1514918 square inches.

The rectangle is 141.4213562

The circle is 39.26990817

May 19th, 2010 at 1:31 pm

hmmmmm

i dont see where youre coming from ragnot

I got the rectangles area to be 100(given sqrt(50)=5*sqrt(2), divided by two and multiplied by sqrt 2 to get the hypotenuse of that triangle, equaling 5, 5*20=100), the circles area to be 12.5*pi

and the remaining area of the rectangle not covered by the circle(keep in mind some of the circle does not cover the rectangle) to be half the circle and two isoceles right triangles formed with the right angle at the center of the circle and the hypotenuse is on the edge of the rectangle

so 100 – (12.5*pi)/2 – ((2.5*sqrt(2))^2)*2 =

100 – 19.634954 – 25 = 55.3650459

May 20th, 2010 at 5:13 am

The radius of the disc is sqrt(50)/2 = r ≈ 3.5355 and r² = 12.5. The

width of the rectangle is sqrt(r² + r²) = 5. The total area of the

rectangle is 5*20 = 100. The area of the disc overlapping the

rectangle is πr²/2 – 2(r²/2) = (π/2 – 1)r² ≈ 7.13495 ; the first part

is due to the to pie slices and the second part is due to the two

triangles. So the uncovered area is is approx 92.865 in².

May 21st, 2010 at 6:14 am

Aaargh, I subtracted when I should have added:

The radius of the disc is sqrt(50)/2 = r ≈ 3.5355 and r² = 12.5. The

width of the rectangle is sqrt(r² + r²) = 5. The total area of the

rectangle is 5*20 = 100. The area of the disc overlapping the

rectangle is πr²/2 + 2(r²/2) = (π/2 + 1)r² ≈ 32.13495 ; the first part

is due to the to pie slices and the second part is due to the two

triangles. So the uncovered area is is approx 67.865 in².

May 26th, 2010 at 11:46 am

Answer is 100.

The two drawn diameters are at right angles.

A triangle can be drawn with two of the radii at right angles and the hypotenuse equal to the width of the rectangle. The radius = 1/2 sqrt(50).

a^2 + b^2 = c^2

then (sqrt50/2)^2 + (sqrt50/2)^2 = c^2

then 50/4 + 50/4 = c^2

then 25 = c^2

so c =5 = width of rectangle

length is 20

so area is 100.

May 28th, 2010 at 3:04 pm

Hi Chris Z. You have found the area of the entire rectangle. The question asks for the uncovered area.