Question

what is the surface area? 10 in, 7 in, 5 in (diagram of a net, handwritten = 310)

Explanation:

Step1: Identify the shape (a rectangular prism net)

The figure is a net of a rectangular prism. The formula for the surface area of a rectangular prism is \( SA = 2(lw + lh + wh) \), where \( l \), \( w \), and \( h \) are length, width, and height. From the net, we can see the dimensions: length \( l = 10 \) in, width \( w = 5 \) in, height \( h = 7 \) in.

Step2: Calculate each pair of faces

First, calculate \( lw \): \( 10\times5 = 50 \)
Then, \( lh \): \( 10\times7 = 70 \)
Then, \( wh \): \( 5\times7 = 35 \)

Step3: Apply the surface area formula

Substitute into the formula: \( SA = 2(50 + 70 + 35) \)
First, add inside the parentheses: \( 50 + 70 + 35 = 155 \)
Then, multiply by 2: \( 2\times155 = 310 \)

Answer:

The surface area is 310 square inches.