Question

Is the answer for this 647 ft^2

Can you help me figure it out the formula is 1/2 multiplied by base multiplied by height
(1/2 x b x h)

Answer 1

`\sf LSA = 448 \, \textsf{square inches}`

`\sf TSA = 544 \, \textsf{square inches}`

Explanation:

There are two types of areas in the triangular prism.

They are Lateral and Total surface area.

Let's calculate Lateral and Total Surface Area of Triangular Prism

Lateral Surface Area (LSA):

The lateral surface area of a triangular prism is the sum of the area of the three rectangular faces. We can calculate it using two formulas:

1. Formula 1:

`\sf LSA = (a + b + c) * h`

where:

`\sf a, b, c` are the sides of the triangular base

`\sf h` is the height of the prism (which is also the length in this case)

2. Formula 2:

`\sf LSA = \textsf{Perimeter of base} * h`

where:

`\sf \textsf{Perimeter of base} = a + b + c`

Using formula 1:

`\sf LSA = (12 + 10 + 10) * 14`

`\sf LSA = 32 * 14`

`\sf LSA = 448 \, \textsf{square inches}`

Using formula 2:

`\sf LSA = (12 + 10 + 10) * 14`

`\sf LSA = 32 * 14`

`\sf LSA = 448 \, \textsf{square inches}`

Therefore, the lateral surface area of the triangular prism is 448 square inches.

Total Surface Area (TSA):

The total surface area of a triangular prism is the sum of the lateral surface area and the area of the two triangular bases.

`\sf TSA = LSA + 2 * \textsf{Area of base}`

Area of base:

`\sf \textsf{Area of base} = 0.5 * \textsf{base} * \textsf{height}`

`\sf \textsf{Area of base} = 0.5 * (12 * 8)`

`\sf \textsf{Area of base} =48 \, \textsf{square inches}`

Total Surface Area:

`\sf TSA = 448 + 2 * 48`

`\sf TSA = 448 + 96`

`\sf TSA = 544 \, \textsf{square inches}`

Therefore, the total surface area of the triangular prism is 544 square inches.