Question

1. A piece of chocolate candy, composed of two congruent triangular prisms like the one shown below, is filled with caramel.


Note: Figure is not drawn to scale.

If a = 1.9 cm, b = 1.2 cm, and c = 2.4 cm, how much caramel can fit inside the piece of candy?
4.332 cu cm
5.5 cu cm
2.736 cu cm
5.472 cu cm

Answer 1

https://app149.studyisland.com/pics/251698num3.png

Answer 2

It's a rectangular prism..find the length and height.

Answer 3

5.5 lol

Answer 4

Take half of 'a'

1.9 / 2 = ?

Answer 5

u have to add all the sides

Answer 6

@!MilitaryLad! Please do not give answers, it's against OpenStudy's Code-of-Conduct. We are here to guide the asker to the answer, so we need his/her participation.

Please read the \(\bf\color{blue}{\underline{{\href{http:///openstudy.com/code-of-conduct}{Code-of-Conduct}}}}\) to learn more.

Answer 7

That's incorrect also..

Answer 8

sorry////-_-

Answer 9

i think u have to multiply them all together...qhich would give u the last one lol

Answer 10

it was 5.472

Answer 11

yep

Answer 12

Yep, you got it.

Answer 13

Would you like to know how to get it?

Answer 14

thnx

Answer 15

B is the opposite side of a right triangle.

A is twice the measurement of the adjacent of that triangle.

So we divide A's measurement by 2:

1.9 / 2 = 0.95

So we have a right triangle with two leg lengths of 0.95 and 1.2.

Plug it in the Pythagorean Theorem to find the hypotenuse, which is also the height of our rectangular prism.

\(\sf a^2 + b^2 = c^2\)

\(\sf 0.95^2 + 1.2^2 = c^2\)

Simplify:

\(\sf 0.9025 + 1.44 = c^2\)

Add:

\(\sf 2.3425 = c^2\)

Find the square root of both sides:

\(\sf c = \sqrt{2.3425}\)

\(\sf c \approx 1.53\)

Now we have the height of the rectangular prism, and this is also the opposite side of a bigger triangle.

So we have 'a' which is 1.9, and our new measurement 1.53, and we need to find the other leg.

\(\sf a^2 = b^2 = c^2\)

\(\sf a^2 + 1.53^2 = 1.9^2\)

Simplify:

\(\sf a^2 + 2.3409 = 3.61\)

Subtract 2.3409 to both sides:

\(\sf a^2 = 1.2691\)

Find the square root of both sides:

\(\sf a = \sqrt{1.2691}\)

\(\sf a \approx 1.13\)

So we have 2.4, 1.13, and 1.53.

Multiply them all:

\(\sf 2.4 \times 1.13 \times 1.53 = 4.14936\)

Oh well..that's wrong..xD