Question

Please help me with the question below (also please explain).

Answer 1

To find the surface area of the given figure identify all the faces on the figure, calculate the area of each face and then sum the areas:

Measures in red

Number of faces in green, total faces 9

Area of a triangle:

$A=\frac{1}{2}bh$

Area of a rectangle:

$A=bh$

Area of faces 1 and 2(rectangles):

$\begin{gathered} A_1=A_2=20in*11in \\ A_1=A_2=220in^2 \end{gathered}$

Area of faces 3 and 4 (triangles):

$\begin{gathered} A_3=A_4=\frac{1}{2}(12in)(9in) \\ \\ A_3=A_4=54in^2 \end{gathered}$

Area of faces 5 and 6 (rectangles):

$\begin{gathered} A_5=A_6=12in*5in \\ A_5=A_6=60in^2 \end{gathered}$

Area of faces 7 and 8 (rectangles):

$\begin{gathered} A_7=A_8=20in*5in \\ A_7=A_8=100in^2 \end{gathered}$

Are of face 9 (rectangle):

$\begin{gathered} A_9=20in*12in \\ A_9=240in^2 \end{gathered}$

Total surface area:

$\begin{gathered} SA=A_1+A_2+A_3+A_4+A_5+A_6+A_7+A_8+A_9 \\ \\ SA=220in^2+220in^2+54in^2+54in^2+60in^2+60in^2+100in^2+100in^2+240in^2 \\ \\ SA=1108in^2 \end{gathered}$

Then, the surface area of the given figure is 1108 square inches