Question

Help in geometry!

Answer 1

A rectangle is inscribed within a circle. The coordinates are (-2,3); (16,3); (-2,5); and (16,-5). What is the area and circumference of the circle?

Answer 2

@e.mccormick

Answer 3

Have you considered the relationship of the diameter of the circle to the diagonal of the rectangle?

Answer 4

okay i figured out thee answer, but how can i check my work? @tkhunny

Answer 5

Not if you don't post it.

Answer 6

for Circumference I got 19.7pi and for area i got pi(9.85)^2

Answer 7

How did you get those?

Answer 8

by subtracting -2 from 16 and -5 from 3 which will give me 18 and 8 in absolute value. Then I used the pythagoean theorom. After that I squared root my answer to give me the diameter

Answer 9

That's not bad, but we have a little data problem.

(-2,3); (16,3); (-2,5); and (16,-5).

Are you SURE it's (-2,5) and not (-2,-5)

Are you SURE it's (16,-5) and not (16,5)

Make sure your figure is a rectangle and not just some old trapezoid.

Answer 10

oopps my bad, its (-2,-5)

Answer 11

it is (16,-5) though

Answer 12

Fair enough.

I might want you to notice that \(\sqrt{388} = 2\sqrt{97}\).

This makes the circumference \(2\pi\sqrt{97}\), still not very pretty, and
the Area \(\pi(\sqrt{97})^2 = 97\pi\).

Answer 13

how did you get 97?

Answer 14

so then this means my answer was wrong?

Answer 15

No, if you like the decimals, yours is fine. If you are alert and happen to notice that \(\sqrt{388} = 2\sqrt{97}\), then you can write exact answers.

\(\sqrt{97}^{2} = 97\)

Answer 16

oh okay. thanks