Question

I need help please and thank you

Answer 1

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 $\frac{1}{2}$ with the product of the base length and it's height.

Area of 1 triangle = $\frac{1}{2} (9)(6)= 27$ cm².

Area of both triangles = Area of 1 triangle × 2 = $27(2)$ = 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 = $5(7)=35$ cm².

Area of the rectangle with width 7 cm = $5(7)=35$ cm².

Area of the rectangle with width 9 cm = $5(9)= 45$ cm².

Step 4:

The area of the entire triangular prism = Area of 2 triangles + Area of all the 3 rectangles = $54 + 35 + 35 + 45$ = 169 cm².