BRAINLIEST A candy bar box is in the shape of a triangular prism. The volume of the box is 1,200 cubic centimetres. 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 base? Show your work. (5 points) Part B: What is the approximate amount of cardboard used to make the candy box? Explain how you got your answer. (5 points)

A- 12 B-840

Step-by-step explanation:

Bottom Layer:

5(10/2), 13, and __            __= 12                     Pythagorean theorom

A - 12

B - How thick is the cardboard? - Is it a solid?

Thinking the cardboard is 1cm thick

top and bottom (10*12/2) *2 = 120 area of top and bottom

two equal sides: 13*20*2=520

Other side: 10*20=200

120+520+200=840

B-840

Hope that helps, tell me if you need further info

Part A: 12 cm

Part B: 840 cm^2

Step-by-step explanation:

Part A:

Draw an isosceles triangle with a horizontal base 10 cm long and two sides 13 cm long. Now draw a segment from the vertex where the two 13-cm sides meet to the midpoint of the 10-cm base. This segment is perpendicular to the base and is the height of the triangle. We need to find its length. The large triangle with 13-cm, 13-cm, and 10-cm sides is now divided into two smaller right triangles. Each of the right triangles has a leg 5 cm long and a 13-cm hypotenuse. The height of the large triangle is the other leg of the smaller triangles.

We now use the Pythagorean theorem:

a^2 + b^2 = c^2

5^2 + b^2 = 13^2

25^2 + b^2 = 169

b^2 = 144

b = 12

The height of the triangular base of the prism is 12 cm long.

Part B:

The amount of cardboard used to make the box is the total surface area of the prism.

total surface area = area of the bases + lateral area

The area of the bases is the sum of the areas of the two bases. Since the two bases are congruent triangle, we multiply the area of one base by 2.

The lateral area is the sum of the area of the three rectangular sides. Two of the rectangles have dimensions 13 cm by 20 cm. One rectangle has dimensions 10 cm by 20 cm.

total surface area = 2 * bh/2 + 2(13 cm * 20 cm) + (10 cm * 20 cm)

total surface area = 2 * (10 cm * 12 cm)/2 + 2(13 cm * 20 cm) + (10 cm * 20 cm)

total surface area = 10 cm * 12 cm + 2(260 cm^2) + 200 cm^2

total surface area = 840 cm^2