Question

find the surface area of the prism using the net. what is the area of the bottom rectangle? front and back triangles: 64 cm² side rectangles: 72 cm² bottom rectangle:? cm² surface area:? cm²

Explanation:

Step1: Identify the dimensions of the bottom rectangle

The bottom rectangle has length 9 cm and width 4 cm.

Step2: Use the rectangle - area formula

The area formula for a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width. Substitute $l = 9$ cm and $w = 4$ cm into the formula: $A=9\times4$.
$A = 36$ $cm^{2}$

Step3: Calculate the surface area of the prism

The surface area $S$ of the prism is the sum of the areas of all its faces. We know the area of the front - and - back triangles is $64$ $cm^{2}$, the area of the side rectangles is $72$ $cm^{2}$, and the area of the bottom rectangle is $36$ $cm^{2}$.
$S=64 + 72+36$
$S = 172$ $cm^{2}$

Answer:

The area of the bottom rectangle is $36$ $cm^{2}$.
The surface area of the prism is $172$ $cm^{2}$.