Question

find the surface area of the lower prism. 10 cm 5 cm saupper = 260 cm² salower = ? cm² satotal = cm² remember! exclude areas where complex shapes touch.

Explanation:

Step1: Recall surface - area formula for a rectangular prism

The surface - area formula for a rectangular prism is $SA = 2(lw+lh + wh)$. For the lower prism with length $l = 13$ cm, width $w = 7$ cm, and height $h = 5$ cm, the surface - area formula gives $SA=2(13\times7 + 13\times5+7\times5)$.

Step2: Calculate the products inside the parentheses

First, calculate $13\times7 = 91$, $13\times5 = 65$, and $7\times5 = 35$. Then $13\times7+13\times5 + 7\times5=91 + 65+35=191$.

Step3: Multiply by 2

$SA = 2\times191=382$ cm². But we need to exclude the area where the two prisms touch. The area of the touching - face (the base of the upper prism) is $10\times5 = 50$ cm². So the surface area of the lower prism $SA_{lower}=382-50 = 332$ cm².

Answer:

$332$