page 14 of 14

Question

Surface Area of Triangular Prisms Quick Check
5 of 55 of 5 Items

Question
Use the image to answer the question.

An illustration shows a triangular prism. The front triangular face is visible. The right rectangular face is visible. The sides and edges that are not visible are indicated by dashed lines. Parts are labeled with measurements. The left side of the triangle measures 10 centimeters. The right side of the triangle also measures 10 centimeters. The perpendicular height from the top vertex of the triangle to the base measures 6 centimeters. The base of the triangle measures 8 centimeters.

What is the missing length l
of the triangular prism if the surface area is 524 square centimeters?

(1 point)
Responses

8 cm
8 cm

16 cm
16 cm

17 cm
17 cm

10 cm
10 cm
Skip to navigation

Answer 1

To find the missing length \( l \) of the triangular prism given that the surface area is 524 square centimeters, we can use the formula for the surface area of a triangular prism, which is:

\[ \text{Surface Area} = (2 \times \text{Area of Triangular Base}) + (\text{Perimeter of the Base} \times l) \]

1. Calculate the area of the triangular base: The base of the triangle is \( 8 \) cm, the height is \( 6 \) cm, and we can calculate the area using the formula:

   \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 6 = 24 \text{ cm}^2 \]

2. Calculate the perimeter of the triangular base: The sides of the triangle measure \( 10 \) cm, \( 10 \) cm, and \( 8 \) cm, hence the perimeter \( P \) is:

   \[ P = 10 + 10 + 8 = 28 \text{ cm} \]

3. Substitute the values into the surface area formula:

   \[ \text{Surface Area} = 2 \times 24 + (28 \times l) \]

   Set the surface area to \( 524 \):

   \[ 524 = 48 + 28l \]

4. Solve for \( l \):

   \[ 524 - 48 = 28l \]

   \[ 476 = 28l \]

   \[ l = \frac{476}{28} = 17 \text{ cm} \]

Thus, the missing length \( l \) of the triangular prism is 17 cm.