Question

surface area of rectangular prisms bell ringer: 1. a right triangle has a hypotenuse length of 20 inches and a leg with a length of 10 inches. what is the length of the other leg rounded to the nearest tenths. today 2. find the surface area. diagram of a rectangular prism with dimensions 22 ft, 9 ft, 6.5 ft 3. find the lateral surface area. diagram of a cube with side 9 m 4. find the lateral surface area. diagram of a rectangular prism with dimensions 20 in, 15 in, 10 in 5. find the surface area. diagram of a rectangular prism with dimensions 16 cm, 8 cm, 5 cm

Explanation:

Problem 3: Lateral Surface Area of a Cube (9m x 9m x 9m)

Step 1: Recall the formula for lateral surface area (LSA) of a cube.

For a cube with side length \( s \), the lateral surface area is given by \( \text{LSA} = 4s^2 \) (since a cube has 4 lateral faces, each with area \( s^2 \)).

Step 2: Substitute the given side length.

Here, \( s = 9 \, \text{m} \). Plugging into the formula:
\( \text{LSA} = 4 \times (9)^2 \)

Step 3: Calculate the value.

First, \( 9^2 = 81 \). Then, \( 4 \times 81 = 324 \).

Step 1: Recall the formula for surface area (SA) of a rectangular prism.

The formula is \( \text{SA} = 2(lw + lh + wh) \), where \( l \) = length, \( w \) = width, \( h \) = height.

Step 2: Identify the dimensions.

Here, \( l = 16 \, \text{cm} \), \( w = 8 \, \text{cm} \), \( h = 5 \, \text{cm} \).

Step 3: Substitute into the formula.

Calculate each term:
\( lw = 16 \times 8 = 128 \)
\( lh = 16 \times 5 = 80 \)
\( wh = 8 \times 5 = 40 \)

Then, \( \text{SA} = 2(128 + 80 + 40) \)

Step 4: Simplify the expression.

First, add inside the parentheses: \( 128 + 80 + 40 = 248 \).
Then, multiply by 2: \( 2 \times 248 = 496 \).

Answer:

The lateral surface area is \( 324 \, \text{m}^2 \).

Problem 5: Surface Area of a Rectangular Prism (16cm x 8cm x 5cm)