The tin game's surface area 177 inch².
Step-by-step explanation:
Step 1:
To calculate the triangular prism's surface area, we calculate the areas of all the 5 sides.
We divide the prism into 2 triangles and 3 rectangles, find the area individually and then sum them all up in order to determine the entire triangular prism's area.
Step 2:
There are two triangles with base lengths of 10 inches and heights of 8.7 inches. To calculate a triangle's area we multiply [tex]\frac{1}{2}[/tex] with the product of the base length and it's height.
Area of 1 triangle = [tex]\frac{10(8.7)}{2} =43.5[/tex] inch².
Area of both triangles = Area of 1 triangle × 2 = [tex]43.5 (2)[/tex] = 87 inch².
Step 3:
There are three rectangles with a common length of 10 inches and a width of 3 inches.
Any rectangle's area is given by multiplying the rectangle's length with its width.
Area of the 1 rectangle = [tex]10(3) = 30[/tex] inch².
Area of 3 rectangles = [tex]3(30) = 90[/tex] inch².
Step 4:
The area of the entire triangular prism = [tex]87+90= 177[/tex] inch².
