What is the surface area of the prism having the base area $25 \, \text{m}^2$ , base perimeter $24 \, \text{m}$ and length $12\,\text{m}$ ?

Full solution

Q. What is the surface area of the prism having the base area

25 \, \text{m}^2

, base perimeter

24 \, \text{m}

and length

12\,\text{m}

Understand formula for surface area: Understand the formula for the surface area of a prism. $\newline$ The surface area of a prism is the sum of the areas of all the faces. For a prism with a polygonal base, the surface area (SA) can be calculated using the formula: $\newline$ $SA = 2 \times \text{base area} + \text{base perimeter} \times \text{length}$
Plug in given values: Plug in the given values into the surface area formula. $\newline$ Given base area $B = 25 \, \text{m}^2$ , base perimeter $P = 24 \, \text{m}$ , and length $l = 12 \, \text{m}$ , we can substitute these values into the formula: $\newline$ $SA = 2 \times 25 \, \text{m}^2 + 24 \, \text{m} \times 12 \, \text{m}$
Calculate surface area: Calculate the surface area. $\newline$ First, calculate the area of the two bases: $\newline$ $2 \times 25 \, \text{m}^2 = 50 \, \text{m}^2$ $\newline$ Then, calculate the lateral surface area: $\newline$ $24 \, \text{m} \times 12 \, \text{m} = 288 \, \text{m}^2$ $\newline$ Now, add these two areas to get the total surface area: $\newline$ $\text{SA} = 50 \, \text{m}^2 + 288 \, \text{m}^2 = 338 \, \text{m}^2$