What is the surface area of a right rectangular prism where each edge length measures 15.10 cm?(1 point)

To find the surface area of a right rectangular prism (also known as a rectangular box), you can use the formula:

\[ \text{Surface Area} = 2(lw + lh + wh) \]

where \(l\), \(w\), and \(h\) are the lengths of the edges of the prism.

In this case, since each edge length measures 15.10 cm, we can let \(l = 15.10\), \(w = 15.10\), and \(h = 15.10\).

Now, substitute these values into the formula:

\[ \text{Surface Area} = 2(15.10 \times 15.10 + 15.10 \times 15.10 + 15.10 \times 15.10) \]

Calculating each term:

\[ 15.10 \times 15.10 = 228.01 \]

So we have:

\[ \text{Surface Area} = 2(228.01 + 228.01 + 228.01) = 2(684.03) = 1368.06 \text{ cm}^2 \]

Therefore, the surface area of the right rectangular prism is 1,368.06 cm².

A carry-on suitcase is 9.5 inches long, 16 inches wide, and 22.5 inches high. What is the surface area of the suitcase

To find the surface area of a rectangular prism (which includes the suitcase), we use the formula:

\[ \text{Surface Area} = 2(lw + lh + wh) \]

where \(l\) is the length, \(w\) is the width, and \(h\) is the height.

Given:

• Length \(l = 9.5\) inches
• Width \(w = 16\) inches
• Height \(h = 22.5\) inches

Let's substitute these values into the formula:

1. Calculate the area of each pair of opposite faces:

   • \(lw = 9.5 \times 16 = 152\) square inches
   • \(lh = 9.5 \times 22.5 = 213.75\) square inches
   • \(wh = 16 \times 22.5 = 360\) square inches

2. Sum these area values: \[ lw + lh + wh = 152 + 213.75 + 360 = 725.75 \text{ square inches} \]

3. Multiply by 2 to get the total surface area: \[ \text{Surface Area} = 2(725.75) = 1451.5 \text{ square inches} \]

Thus, the surface area of the suitcase is 1451.5 square inches.

Find the surface area of a rectangular pyramid with these measurements: l
= 15 m, w
= 12 m, and h
= 10 m.

To find the surface area of a rectangular pyramid, we need to consider the base area and the areas of the triangular faces.

1. Base Area: The base of the pyramid is a rectangle, so the area of the base is given by: \[ \text{Base Area} = l \times w \] Using \(l = 15\) m and \(w = 12\) m: \[ \text{Base Area} = 15 \times 12 = 180 \text{ m}^2 \]

2. Lateral Surface Area: The pyramid has four triangular faces. To find the area of these faces, we first need to find the slant heights of the triangles.

   The slant height \(s\) can be calculated using the Pythagorean theorem. We have half of the length and width to get the horizontal distance from the center of the base to the midpoint of each side:

   • Half the length: \( \frac{l}{2} = \frac{15}{2} = 7.5\) m
   • Half the width: \( \frac{w}{2} = \frac{12}{2} = 6\) m

   We find the slant height of the triangular faces using: \[ s = \sqrt{h^2 + \left(\frac{w}{2}\right)^2} \quad \text{and} \quad s = \sqrt{h^2 + \left(\frac{l}{2}\right)^2} \]

   Calculate the slant heights for two pairs of triangular faces:

   For the faces opposite the width: \[ s_w = \sqrt{10^2 + 7.5^2} = \sqrt{100 + 56.25} = \sqrt{156.25} \approx 12.5 \text{ m} \]

   For the faces opposite the length: \[ s_l = \sqrt{10^2 + 6^2} = \sqrt{100 + 36} = \sqrt{136} \approx 11.66 \text{ m} \]

3. Area of the Triangular Faces: The area of one triangular face is given by: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]

   • For the width sides: \[ \text{Area of one triangle (width)} = \frac{1}{2} \times 12 \times 12.5 = \frac{1}{2} \times 12 \times 12.5 = 75 \text{ m}^2 \]

   • There are two triangles for the width: \[ \text{Total area for width sides} = 2 \times 75 = 150 \text{ m}^2 \]

   • For the length sides: \[ \text{Area of one triangle (length)} = \frac{1}{2} \times 15 \times 11.66 \approx \frac{1}{2} \times 15 \times 11.66 \approx 87.45 \text{ m}^2 \]

   • There are two triangles for the length: \[ \text{Total area for length sides} = 2 \times 87.45 \approx 174.9 \text{ m}^2 \]

4. Total Lateral Surface Area: \[ \text{Lateral Surface Area} = \text{Total area for width sides} + \text{Total area for length sides} = 150 + 174.9 \approx 324.9 \text{ m}^2 \]

5. Total Surface Area: The total surface area is the sum of the base area and the lateral surface area: \[ \text{Total Surface Area} = \text{Base Area} + \text{Lateral Surface Area} = 180 + 324.9 \approx 504.9 \text{ m}^2 \]

Thus, the surface area of the rectangular pyramid is approximately 504.9 m².

round answer to the hundreth

Rounding the total surface area of the rectangular pyramid to the hundredths place:

The calculated surface area is approximately 504.9 m².

Rounding this to the hundredths place results in:

\[ \text{Total Surface Area} \approx 504.90 \text{ m}^2 \]

So, the final answer, rounded to the hundredths place, is 504.90 m².