Answer:
[tex]a.\ \ \ A=684\ m^2[/tex]
[tex]b.\ \ \ A=130.2 \ km^2[/tex]
Step-by-step explanation:
a. Area is calculated by summing the areas of the prism's individual surfaces.
#First, calculate the areas of the right-angled surfaces:
[tex]Area=2(\frac{1}{2}bh), b=9, h=12\\\\=2\times \frac{1}{2}\times 9\times 12\\\\=108\ m^2[/tex]
#We then find the areas of the rectangular surfaces:
[tex]A=lw\\\\=15\times 16+9\times 16+16\times 12\\\\=576\ m^2[/tex]
#We sum the areas to find the total surface areas:
[tex]A=\sum{Areas_i}\\\\=108+576\\\\=684\ m^2[/tex]
Hence, the prism's surface area is [tex]684\ m^2[/tex]
b.Area is calculated by summing the areas of the prism's individual surfaces.
#First, calculate the areas of the right-angled surfaces:
[tex]A=2\times \frac{1}{2}bh,\ b=12, h=4.1\\\\=2\times 0.5\times 12\times 4.1\\\\=49.2 \ km^2[/tex]
#We then find the areas of the rectangular surfaces:
[tex]A=lw\\\\=5\times 3+3\times 10+12\times 3\\\\=81\ km^2[/tex]
#We sum the areas to find the total surface areas:
[tex]A=A_r+A_t\\\\=81+49.2\\\\=130.2 \ km^2[/tex]
Hence, the prism's surface area is [tex]130.2 \ km^2[/tex]
