### Geometry Problems on Hexagonal Prism and Pyramid**Problem 1:****a)** Find the total surface area $ T $ of a hexagonal right prism with base edge 4 and altitude 5.**Solution:**For a hexagonal right prism, the total surface area $ T $ can be found by adding the areas of the two hexagonal bases and the six rectangular faces.1. Calculate the area of one hexagonal base.2. Multiply the area by 2 (since there are two bases).3. Calculate the area of one rectangular face.4. Multiply the area of the rectangular face by 6 (since there are six faces).**Problem 2:****b)** Find the volume of a right hexagonal pyramid with base edge 4 and altitude 2.**Solution:**To find the volume of a hexagonal pyramid, use the formula for the volume of a pyramid: $\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height}$.1. Calculate the area of the hexagonal base.2. Use the given altitude for the pyramid's height.3. Apply the formula to find the volume.These problems require understanding of geometric formulas and the properties of hexagonal shapes. Detailed calculations and explanations are necessary to derive the answers.

To find the area and volume of a hexagonal prism:

Answered: 12 a) Find the Total u T of a with base…

12 a) Find the Total u T of a with base edge 4 and hexagonal ight prism altitue 5. b) Find the Volume of a with base edge 4 and altinde 2. naht hexagonul pyramid

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

### Geometry Problems on Hexagonal Prism and Pyramid

**Problem 1:**
**a)** Find the total surface area $ T $ of a hexagonal right prism with base edge 4 and altitude 5.

**Solution:**
For a hexagonal right prism, the total surface area $ T $ can be found by adding the areas of the two hexagonal bases and the six rectangular faces.

1. Calculate the area of one hexagonal base.
2. Multiply the area by 2 (since there are two bases).
3. Calculate the area of one rectangular face.
4. Multiply the area of the rectangular face by 6 (since there are six faces).

**Problem 2:**
**b)** Find the volume of a right hexagonal pyramid with base edge 4 and altitude 2.

**Solution:**
To find the volume of a hexagonal pyramid, use the formula for the volume of a pyramid: $\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height}$.

1. Calculate the area of the hexagonal base.
2. Use the given altitude for the pyramid's height.
3. Apply the formula to find the volume.

These problems require understanding of geometric formulas and the properties of hexagonal shapes. Detailed calculations and explanations are necessary to derive the answers.

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