Question

2.
lateral area:
15 cm
total surface area:
4 cm
4 cm
4.
lateral area:
27 yd
total surface area:
10 yd
16 yd

Explanation:

Problem 2 (Rectangular Prism with dimensions 4 cm, 4 cm, 15 cm)

Lateral Area of a Rectangular Prism

The formula for the lateral area \( LA \) of a rectangular prism is \( LA = 2h(l + w) \), where \( l \) is length, \( w \) is width, and \( h \) is height.

Step 1: Identify the dimensions

Here, \( l = 4 \) cm, \( w = 4 \) cm, \( h = 15 \) cm.

Step 2: Substitute into the lateral area formula

\( LA = 2 \times 15 \times (4 + 4) \)
\( LA = 30 \times 8 \)
\( LA = 240 \) \( cm^2 \)

Total Surface Area of a Rectangular Prism

The formula for the total surface area \( TSA \) is \( TSA = 2(lw + lh + wh) \).

Step 1: Substitute the dimensions

\( TSA = 2(4 \times 4 + 4 \times 15 + 4 \times 15) \)
\( TSA = 2(16 + 60 + 60) \)
\( TSA = 2(136) \)
\( TSA = 272 \) \( cm^2 \)

Problem 4 (Rectangular Prism with dimensions 16 yd, 10 yd, 27 yd)

Lateral Area of a Rectangular Prism

Using the formula \( LA = 2h(l + w) \), where \( l = 16 \) yd, \( w = 10 \) yd, \( h = 27 \) yd.

Step 1: Substitute into the lateral area formula

\( LA = 2 \times 27 \times (16 + 10) \)
\( LA = 54 \times 26 \)
\( LA = 1404 \) \( yd^2 \)

Total Surface Area of a Rectangular Prism

Using the formula \( TSA = 2(lw + lh + wh) \).

Step 1: Substitute the dimensions

\( TSA = 2(16 \times 10 + 16 \times 27 + 10 \times 27) \)
\( TSA = 2(160 + 432 + 270) \)
\( TSA = 2(862) \)
\( TSA = 1724 \) \( yd^2 \)

Final Answers

Problem 2

• Lateral Area: \( \boldsymbol{240 \ cm^2} \)
• Total Surface Area: \( \boldsymbol{272 \ cm^2} \)

Problem 4

• Lateral Area: \( \boldsymbol{1404 \ yd^2} \)
• Total Surface Area: \( \boldsymbol{1724 \ yd^2} \)

Answer:

Problem 2 (Rectangular Prism with dimensions 4 cm, 4 cm, 15 cm)

Lateral Area of a Rectangular Prism

The formula for the lateral area \( LA \) of a rectangular prism is \( LA = 2h(l + w) \), where \( l \) is length, \( w \) is width, and \( h \) is height.

Step 1: Identify the dimensions

Here, \( l = 4 \) cm, \( w = 4 \) cm, \( h = 15 \) cm.

Step 2: Substitute into the lateral area formula

\( LA = 2 \times 15 \times (4 + 4) \)
\( LA = 30 \times 8 \)
\( LA = 240 \) \( cm^2 \)

Total Surface Area of a Rectangular Prism

The formula for the total surface area \( TSA \) is \( TSA = 2(lw + lh + wh) \).

Step 1: Substitute the dimensions

\( TSA = 2(4 \times 4 + 4 \times 15 + 4 \times 15) \)
\( TSA = 2(16 + 60 + 60) \)
\( TSA = 2(136) \)
\( TSA = 272 \) \( cm^2 \)

Problem 4 (Rectangular Prism with dimensions 16 yd, 10 yd, 27 yd)

Lateral Area of a Rectangular Prism

Using the formula \( LA = 2h(l + w) \), where \( l = 16 \) yd, \( w = 10 \) yd, \( h = 27 \) yd.

Step 1: Substitute into the lateral area formula

\( LA = 2 \times 27 \times (16 + 10) \)
\( LA = 54 \times 26 \)
\( LA = 1404 \) \( yd^2 \)

Total Surface Area of a Rectangular Prism

Using the formula \( TSA = 2(lw + lh + wh) \).

Step 1: Substitute the dimensions

\( TSA = 2(16 \times 10 + 16 \times 27 + 10 \times 27) \)
\( TSA = 2(160 + 432 + 270) \)
\( TSA = 2(862) \)
\( TSA = 1724 \) \( yd^2 \)

Final Answers

Problem 2

• Lateral Area: \( \boldsymbol{240 \ cm^2} \)
• Total Surface Area: \( \boldsymbol{272 \ cm^2} \)

Problem 4

• Lateral Area: \( \boldsymbol{1404 \ yd^2} \)
• Total Surface Area: \( \boldsymbol{1724 \ yd^2} \)