Question

Find the surface area and the volume of the figure shown. Note that the figure may not be drawn to scale.7d2 yd9 ydThe surface area of the figure isM (Simplify your answer.)The volume of the figure isV (Simplify your answer.)

Answer 1

In order to find the surface area we need to calculate the area of each face

We have two faces with his shape

`A_1=(2\cdot9)+(3\cdot2)=24yd^2`

then we have rectangles in the other faces the formula of the area of a rectangle is l times w where l is the length and w is the width

where A2 is the bottom face and A7 is the lateral face that we can't see in the image but we know they exist

`A_2=9\cdot12=108yd^2`
`A_3=12\cdot2=24yd^2`
`A_4=7\cdot12=84yd^2`
`A_5=3\cdot12=36yd^2`
`A_6=2\cdot12=24yd^2`
`A_7=5\cdot12=60yd^2_{}`

In order to calculate the surface area we sum all the areas we found remember we have 2 faces with the A1

`\begin{gathered} SA=2A_1+A_2+A_3+A_4+A_5+A_6+A_7_{} \\ \end{gathered}`

we substitute the values

`SA=2(24)+108+24+84+3624+60=384yd^2`

The surface area of the figure is 384 yd^2

Then for the volume, we have the next formula

`V=A_1\cdot w`

where

A1=24yd^2

w=12yd

we substitute the values

`V=24\cdot12=288yd^3`

the volume of the figure is 288yd^3