What is the answer to this **Title: Calculating the Surface Area of a Triangular Prism Using Its Net****Objective:**Learn how to find the surface area of a triangular prism by analyzing its net.**Problem Statement:**Using the net below, find the surface area of the triangular prism.**Diagram Description:**The provided diagram shows the net of a triangular prism with the following dimensions:- Two right-angled triangles with legs of 4 cm and 5 cm, and a hypotenuse of 6 cm.- Three rectangular faces: - Two rectangles of dimensions 8 cm by 5 cm. - One rectangle of dimensions 8 cm by 6 cm.**Net Dimensions:**1. Rectangular Faces: - Two rectangles: - Length: 8 cm - Width: 5 cm - One rectangle: - Length: 8 cm - Width: 6 cm2. Triangular Faces: - Base: 6 cm - Height: 4 cm - Hypotenuse: 5 cm**Steps to Calculate Surface Area:**1. Calculate the area of the triangular faces: - Area of one triangle = \(\frac{1}{2} \times \text{base} \times \text{height}\) - For one triangle: \(\frac{1}{2} \times 6 \, \text{cm} \times 4 \, \text{cm}\) = 12 \( \text{cm}^2\) - Since there are two identical triangular faces, their total area = \(2 \times 12 \text{cm}^2\) = 24 \( \text{cm}^2\)2. Calculate the area of the rectangular faces: - Area of each 8 cm by 5 cm rectangle = \(8 \, \text{cm} \times 5 \, \text{cm} = 40 \, \text{cm}^2\) - There are two such rectangles, so their total area = \(2 \times 40 \, \text{cm}^2 = 80 \, \text{cm}^2\) - Area of the 8 cm by 6 cm rectangle = \(8 \, \text{cm} \times 6 \, \text{cm} =

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Answered: Using the net below, find the surface…

Using the net below, find the surface area of the triangular prism. 15 cm 4 cm 8 cm 6 cm 4 cm Surface Area = njh 8 cm [?] cm² 5 cm 5 cm Enter

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.4: Polyhedrons And Spheres

Problem 23E: The surface of a soccer ball is composed of 12 regular pentagons and 20 regular hexagons. With each...

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Question

What is the answer to this

**Title: Calculating the Surface Area of a Triangular Prism Using Its Net**

**Objective:**
Learn how to find the surface area of a triangular prism by analyzing its net.

**Problem Statement:**
Using the net below, find the surface area of the triangular prism.

**Diagram Description:**
The provided diagram shows the net of a triangular prism with the following dimensions:

- Two right-angled triangles with legs of 4 cm and 5 cm, and a hypotenuse of 6 cm.
- Three rectangular faces:
- Two rectangles of dimensions 8 cm by 5 cm.
- One rectangle of dimensions 8 cm by 6 cm.

**Net Dimensions:**
1. Rectangular Faces:
- Two rectangles:
- Length: 8 cm
- Width: 5 cm
- One rectangle:
- Length: 8 cm
- Width: 6 cm

2. Triangular Faces:
- Base: 6 cm
- Height: 4 cm
- Hypotenuse: 5 cm

**Steps to Calculate Surface Area:**
1. Calculate the area of the triangular faces:
- Area of one triangle = \(\frac{1}{2} \times \text{base} \times \text{height}\)
- For one triangle: \(\frac{1}{2} \times 6 \, \text{cm} \times 4 \, \text{cm}\) = 12 \( \text{cm}^2\)
- Since there are two identical triangular faces, their total area = \(2 \times 12 \text{cm}^2\) = 24 \( \text{cm}^2\)

2. Calculate the area of the rectangular faces:
- Area of each 8 cm by 5 cm rectangle = \(8 \, \text{cm} \times 5 \, \text{cm} = 40 \, \text{cm}^2\)
- There are two such rectangles, so their total area = \(2 \times 40 \, \text{cm}^2 = 80 \, \text{cm}^2\)

- Area of the 8 cm by 6 cm rectangle = \(8 \, \text{cm} \times 6 \, \text{cm} =

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