A candy bar box is in the shape of a triangular prism. The volume of the box is 2,400 cubic centimeters.

Part A: What is the height of the base? Show your work.

Part B: What is the approximate amount of cardboard used to make the candy box? Explain how you got your answer.

Part A; The height of the base is 15 cm.

Part B; Approximately 320 cm of cardboard is used to make the candy box.

Step-by-step explanation:

Step 1; We split the triangle into two right-angled triangles. So each triangle has an 8 cm long adjacent side and a 17 cm long hypotenuse. As we have two sides of the triangle, we can solve for the other side's length by using Pythagoras' theorem. Assume the opposite side of the triangle measures x cm. According to Pythagoras theorem, 17² = 8² + x²,

289 = 64 + x², x² = 289 - 64 = 225, x = √225 = 15 cm.

So the height of the base is 15 cm.

Step 2; To find the amount of cardboard needed, we need to determine the perimeter. There are 2 triangular faces and 3 rectangular faces.

A triangle's perimeter is the sum of all the side lengths.

The perimeter of the triangular face = 16 + 17 + 17 = 50 cm.

The perimeter for two triangular faces = 2 × 50 = 100 cm.

Step 3; A rectangle's perimeter is determined by multiplying the rectangle's length with the rectangle's width.

Of the three rectangular faces, two are similar.

The perimeter for the face along the side of the triangle = 2 × (20 + 17) =

2 × 37 = 74 cm.

The perimeter for two similar rectangular planes = 2 × 74 = 148 cm.

The perimeter for the face along the base of the triangle = 2 × (16 + 20) =

2 × 36 = 72 cm.

The perimeter of the entire shape = 100 + 148 + 72 = 320 cm.

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,

sas (side angle side)

aa(angle angle)

sss(side side side)

sas you have to find two sides with an angle in between

aa you find two angles because it will always add up to 180

sss find all sides

step-by-step explanation: