1. The rectangular based pyramid below is NOT drawn to scale. You are given that a = 24 inches, b = 34 inches, and h = 27 inches. a (a) Calculate the surface area of the rectangular based pyramid. Round your final answer to one decimal place if needed. (b) Calculate the volume of the rectangular based pyramid. Round your final answer to one decimal place if needed.
1. The rectangular based pyramid below is NOT drawn to scale. You are given that a = 24 inches, b = 34 inches, and h = 27 inches. a (a) Calculate the surface area of the rectangular based pyramid. Round your final answer to one decimal place if needed. (b) Calculate the volume of the rectangular based pyramid. Round your final answer to one decimal place if needed.
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
![**Problem Statement:**
1. The rectangular based pyramid below is NOT drawn to scale. You are given that \( a = 24 \) inches, \( b = 34 \) inches, and \( h = 27 \) inches.
[Diagram of a rectangular pyramid with labeled dimensions: \( a \), \( b \), \( h \), and slant heights \( h_1 \) and \( h_2 \). The base is a rectangle with sides \( a \) and \( b \). The height \( h \) is the perpendicular distance from the base to the apex.]
**(a)** Calculate the surface area of the rectangular based pyramid. Round your final answer to one decimal place if needed.
**(b)** Calculate the volume of the rectangular based pyramid. Round your final answer to one decimal place if needed.
---
**Explanation of Diagram:**
The diagram shows a rectangular pyramid with a rectangular base and an apex above the center of the base. It illustrates the base dimensions \( a \) and \( b \), the height \( h \) from the center of the base to the apex, and the slant heights \( h_1 \) and \( h_2 \) along the triangular faces. The base is rectangle-shaped with sides labeled \( a \) (24 inches) along the width and \( b \) (34 inches) along the length. The pyramid’s vertical height is given as \( h = 27 \) inches.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F064da53a-967b-4bcd-9e59-024854cda349%2F6d203f7b-3a1b-4e50-8357-b0b46ec999e6%2Fgo9qep_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
1. The rectangular based pyramid below is NOT drawn to scale. You are given that \( a = 24 \) inches, \( b = 34 \) inches, and \( h = 27 \) inches.
[Diagram of a rectangular pyramid with labeled dimensions: \( a \), \( b \), \( h \), and slant heights \( h_1 \) and \( h_2 \). The base is a rectangle with sides \( a \) and \( b \). The height \( h \) is the perpendicular distance from the base to the apex.]
**(a)** Calculate the surface area of the rectangular based pyramid. Round your final answer to one decimal place if needed.
**(b)** Calculate the volume of the rectangular based pyramid. Round your final answer to one decimal place if needed.
---
**Explanation of Diagram:**
The diagram shows a rectangular pyramid with a rectangular base and an apex above the center of the base. It illustrates the base dimensions \( a \) and \( b \), the height \( h \) from the center of the base to the apex, and the slant heights \( h_1 \) and \( h_2 \) along the triangular faces. The base is rectangle-shaped with sides labeled \( a \) (24 inches) along the width and \( b \) (34 inches) along the length. The pyramid’s vertical height is given as \( h = 27 \) inches.
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