Question

The diagram below shows a plane slicing a rectangular prism along the diagonals of its side faces. The shaded figure shows the cross section obtained.



Which is closest to the area of the cross section?

12 square inches

18 square inches

22 square inches

27 square inches

Answer 1

http://puu.sh/2uvBJ

Answer 2

hi can you help me?

Answer 3

Yes.

Answer 4

its a study guide and it is my last question :D

Answer 5

Look at the prism from the front face. This is what you'd see:

Answer 6

okay

Answer 7

If you prefer, call that face the left face. From here you can find the length of x, the diagonal. Then the shaded area is simply x times 3 in.

Answer 8

To find x, notice that since the face of the prism is a rectangle, you have two right triangles. You know the legs of the right triangle measure 4 in. and 6 in. You can find the hypotenuse using the Pythagorean theorem.

Answer 9

can you fresh me up on the Pythagorean theorem, isnt it a + b =c?

Answer 10

which would make it 10?

Answer 11

It's a^2 + b^2 = c^2, not a + b = c. Don't forget the squares.

Answer 12

wah i am lost, is the answer 18?

Answer 13

square inches

Answer 14

First let's the the Pythagoras together:
a^2 + b^2 = c^2. For us, c is the hypotenuse I called x, so
a^2 + b^2 = x^2, but we have a = 6 in. and b = 4 in., so we get
4^2 + 6^2 = x^2
16 + 36 = x^2
x^2 = 52
Since x^2 = 52, we take the square root of 52 to get x.
x = 7.21...

Answer 15

Now to get the area, we multiply 7.21 by 3, to get:
A = 3 in. * 7.21 in. = 21.6 in^2
Which choice is closest to 21.6 square inches?

Answer 16

OHHHH i am an idiot lol its 2 thanks for the help haha

Answer 17

22*

Answer 18

You're welcome.