The prism's surface area 169 cm².
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 9 cm and heights of 6 cm. 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{1}{2} (9)(6)= 27[/tex] cm².
Area of both triangles = Area of 1 triangle × 2 = [tex]27(2)[/tex] = 54 cm².
Step 3:
There are three rectangles with a common length of 5 cm but there are three different widths.
Any rectangle's area is given by multiplying the rectangle's length with its width.
Area of the rectangle with width 7 cm = [tex]5(7)=35[/tex] cm².
Area of the rectangle with width 7 cm = [tex]5(7)=35[/tex] cm².
Area of the rectangle with width 9 cm = [tex]5(9)= 45[/tex] cm².
Step 4:
The area of the entire triangular prism = Area of 2 triangles + Area of all the 3 rectangles = [tex]54 + 35 + 35 + 45[/tex] = 169 cm².
