Question

PLEASE HELP ME IM DESPERATE ILL APPRECITE IT SMM

Answer 1

Surface area of the right prism =
`\sf 31200 \, \textsf{mm}^2`

Explanation:

To calculate the surface area of a right prism with an isosceles triangle as a base, we need to find the areas of the lateral faces and the base.

The surface area
`\sf A` of a right prism is given by the formula:

`\sf A = 2B + Ph`

where:

-
`\sf B` is the area of the base,

-
`\sf P` is the perimeter of the base, and

-
`\sf h` is the height of the prism.

For a right prism with an isosceles triangle as the base, the area
`\sf B` of the base can be found using Heron's formula, which is given by:

`\sf B = √(s(s-a)(s-b)(s-c))`

where
`\sf s` is the semi-perimeter of the triangle, and
`\sf a, b,` and
`\sf c` are the lengths of the triangle sides.

The semi-perimeter
`\sf s` is calculated as:

`\sf s = (a + b + c)/(2)`

Given that the sides of the isosceles triangle are 50mm, 50mm, and 80mm, we can calculate
`\sf s` as:

`\sf s = (50 + 50 + 80)/(2) = 90`

Now, we can find the area
`\sf B` using Heron's formula:

`\sf B = √(90 \cdot (90-50) \cdot (90-50) \cdot (90-80))`

`\sf B = √(90 \cdot 40 \cdot 40 \cdot 10)`

`\sf B = √(1440000)`

`\sf B = 1200 \, \textsf{mm}^2`

Next, calculate the perimeter
`\sf P` of the base:

`\sf P = a + b + c`

`\sf P = 50 + 50 + 80`

`\sf P = 180 \, \textsf{mm}`

Now, substitute these values into the formula for the surface area:

`\sf A = 2 \cdot 1200 + 180 \cdot 160`

`\sf A = 2400 + 28800`

`\sf A = 31200 \, \textsf{mm}^2`

Therefore, the surface area of the right prism is
`\sf 31200 \, \textsf{mm}^2`.