Calculate Circle Area When Rectangle Area = 28X: Geometric Relationship Problem

Question

The area of the rectangle in the drawing is 28X cm².

What is the area of the circle?

00:00 Express the circumference of the circle using X

00:03 The short side is a diameter according to the given data

00:07 We'll use the formula to calculate rectangle area: side(7) multiplied by side(2R)

00:10 We'll substitute appropriate values and solve for R

00:19 We'll isolate R

00:25 This is the expression for radius(R) using X

00:29 Now we'll use the formula to calculate the circle's circumference

00:36 We'll substitute appropriate values and solve to find the circumference expression

00:45 And this is the solution to the question

Let's draw the center of the circle and we can divide the diameter of the circle into two equal radii

Now let's calculate the length of the radii as follows:

$7\times2r=28x$

$14r=28x$

We'll divide both sides by 14:

$r=\frac{28}{14}x$

$r=2x$

Let's calculate the circumference of the circle:

$P=2\pi\times r=2\pi\times2x=4\pi x$

$4\pi x$