Question

Find the surface area and volume of the following solids , a trapezoidal prism with base area 254mm2 , base perimeter 74mm and height 10 mm

Answer 1

The surface area is calculated as

$Total\text{ surface area=side area + top area +base area}$

The side area is calculated as

$\begin{gathered} \text{side area= base perimeter }\times height \\ =74\operatorname{mm}\times10\operatorname{mm}=740\operatorname{mm}^2 \end{gathered}$

The base area and the top area are the same. The base area has been given. Therefore, the total surface area would be

$\begin{gathered} \text{Total surface area =} \\ 740\operatorname{mm}+254\operatorname{mm}+254\operatorname{mm}=1248\operatorname{mm}^2 \end{gathered}$

The volume of the prism would be calculated by

$\begin{gathered} \text{Volume}=\text{Base area }\times height \\ \text{Volume}=254\operatorname{mm}^2\times10\operatorname{mm} \\ =2540\operatorname{mm} \end{gathered}$

Hence, the surface area is 1248mm² and the volume is 2540mm³