Acandy bar box is in the shape of a triangular prism. the volume of the box is 1,200 cubic centimeters. a triangular prism is shown with base of triangle labeled 10 cm, sides of the triangles labeled 13 cm, and length of the box equal to 20 cm. part a: what is the height of the box? show your work. (5 points) part b: what is the approximate amount of cardboard used to make the sides of the candy box? explain how you got your answer. (5 points)

Hello!

As you can see, we see a right triangle on the triangle face of our prism. The hypotenuse is 13 cm, and the base would be 5. We can use the Pythagorean Theorem to find the height.

169-25=144

√144=12

Therefore, our height is 12 cm.

Now we need to find the surface area. First, let's find the base.

20(10)=200

Let's find the two triangular faces

5(13)=65

65(2)=130

Now we find the rectangular faces.

20(13)=260

260(2)=520

Now we add up our final totals.

200+130+520=850

Therefore, they would need 850 cm of cardboard.

I hope this helps!

Height=12

169 - 25 =144

√ 144 =12

The exact amount of cardboard used to make the box is, 850 cm

base=200

both triangular face, 130

Rectanular face, 520

now, we add all of our products 200+130+520= and we will get the sum of 850

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