To find the missing length \( l \) of the triangular prism, we first need to calculate the surface area of the prism.
The surface area of a triangular prism consists of the two triangular faces and the three rectangular faces.
The formula for the surface area of a triangular prism is:
\[ SA = 2 \times (\text{Area of triangle }) + \text{ Perimeter of base } \times \text{ Height of prism} \]
The area of the triangle is calculated as:
\[ 0.5 \times \text{ Base } \times \text{ Height } = 0.5 \times 8 \times 6 = 24 \text{ square cm} \]
The perimeter of the triangle is:
\[ 2 \times 10 + 8 = 28 \text{ cm} \]
Now we can calculate the surface area:
\[ SA = 2 \times 24 + 28 \times l \]
Given that the surface area is 524 square cm, we can substitute this into the equation:
\[ 524 = 48 + 28l \]
\[ 476 = 28l \]
\[ l = \frac{476}{28} \]
\[ l = 17 \text{ cm} \]
Therefore, the missing length of the triangular prism is 17 cm.
The correct response is: 17 cm
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
17 cm
17 cm
16 cm
16 cm
10 cm
10 cm
8 cm
8 cm
Skip to navigation
1 answer
1 answer