Question

Please help with the question below (please try to answer in maximum 10/15 minutes).

Answer 1

Given the dimensions of the composite figure below

`\begin{gathered} For\text{ the cuboid:} \\ l=12\text{cm} \\ w=4\text{ cm} \\ h=3cm \\ For\text{ the triangular prism:} \\ a=3\text{ cm} \\ b=4\text{ cm} \\ c=13\text{ cm} \\ h=5\text{ cm} \end{gathered}`

To find the surface area, SA, of the composite figure, the formula

`SA=2(lh)+2(wh)+(lw)+2((1)/(2)lh)+(bc)+(ah)`

Substitute the values of the variables into the formula above

`\begin{gathered} SA=2\left(12\cdot3\right)+2\left(3\cdot4\right)+\left(12\cdot4\right)+2\left((1)/(2)\left(12\cdot5\right)\right)+\left(13\cdot4\right)+\left(4\cdot5\right) \\ SA=2(36)+2(12)+(48)+(60)+(52)+20 \\ SA=72+24+48+60+52+20 \\ SA=276\text{ cm}^2 \end{gathered}`

Hence, the surface area, SA, is

`276\text{ cm}^2`