Question

surface area of rectangular prisms
determine the lateral and total surface area of triangular prism. round to the nearest tenth i
1.
lateral area:
______
total surface
area:______
4 in.
6 in.
7 in.

Explanation:

Step1: Recall the formula for the lateral surface area (LSA) of a rectangular prism (note: the problem mentions triangular prism but the diagram is a rectangular prism, so we use rectangular prism formulas). The formula for LSA of a rectangular prism is \( LSA = 2h(l + w) \), where \( l \) is length, \( w \) is width, \( h \) is height. Here, \( l = 7 \) in, \( w = 6 \) in, \( h = 4 \) in.

\( LSA = 2\times4\times(7 + 6) \)

Step2: Calculate the lateral surface area. First, compute \( 7 + 6 = 13 \), then \( 2\times4 = 8 \), then \( 8\times13 = 104 \) square inches.

\( LSA = 104 \)

Step3: Recall the formula for total surface area (TSA) of a rectangular prism: \( TSA = 2(lw + lh + wh) \). Substitute \( l = 7 \), \( w = 6 \), \( h = 4 \).

\( TSA = 2\times(7\times6 + 7\times4 + 6\times4) \)

Step4: Calculate each term inside the parentheses. \( 7\times6 = 42 \), \( 7\times4 = 28 \), \( 6\times4 = 24 \). Sum them: \( 42 + 28 + 24 = 94 \). Then multiply by 2: \( 2\times94 = 188 \) square inches.

\( TSA = 188 \)

Answer:

Lateral Area: \( 104 \) square inches
Total Surface Area: \( 188 \) square inches