Pre-Algebra, Student Edition
Pre-Algebra, Student Edition
1st Edition
ISBN: 9780078885150
Author: McGraw-Hill
Publisher: Glencoe/McGraw-Hill
Question
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Chapter 12.7, Problem 29STP
To determine

To find: the slant height of the pyramid

Expert Solution & Answer
Check Mark

Answer to Problem 29STP

The slant height of the square pyramid is 10 m.

Explanation of Solution

Given:

A square pyramid has a base with sides measuring 7 meters. The surface area of the pyramid is 189 square meters.

  1. 8 m
  2. 10 m
  3. 14 m
  4. 16 m

Formula used:

The lateral area Lof a square pyramidis L=12Pl .

Here, P is the perimeter of the base and l is the slant height the square pyramid.

The surface area S of a Square pyramid is S = L + B.

Here, L is the lateral surface area and B is the area of the base.

Calculation:

Consider a square pyramid whose sides length of the base is 7 m and the surface area of the pyramid is 189m2 .

The objective is to find the slant height of the square pyramid.

Find the lateral area of the square pyramid as follows:

The side of the square is 7 m.

The perimeter P of the square is, P = 4 (side).

Substitute side = 7 in P = 4(side).

Thus,

  P=4.7=28

Assume the slant height of the square pyramid is l.

Substitute P=28 in L=12Pl .

  L=12Pl=122814l=14l

Hence, the lateral area L, of a square pyramid is 14l.

Find the surface area of the square pyramid as follows:

The area B of the base is B=(side)2

Substitute side = 7 in B=(side)2

  B=72=49

Substitute B=49, L = 14 l and S = 189 in S = L + B.

  S=L+B189=14l+4918949=14l+4949140=14l14l=140l=14014=10

Hence, the slant height of the square pyramid is 10 m.

Conclusion:

Hence, the option B is the correct one.

Chapter 12 Solutions

Pre-Algebra, Student Edition

Ch. 12.1 - Prob. 7PPSCh. 12.1 - Prob. 8PPSCh. 12.1 - Prob. 9PPSCh. 12.1 - Prob. 10PPSCh. 12.1 - Prob. 11PPSCh. 12.1 - Prob. 12PPSCh. 12.1 - Prob. 13PPSCh. 12.1 - Prob. 14PPSCh. 12.1 - Prob. 15PPSCh. 12.1 - Prob. 16PPSCh. 12.1 - Prob. 17PPSCh. 12.1 - Prob. 18PPSCh. 12.1 - Prob. 19PPSCh. 12.1 - Prob. 20PPSCh. 12.1 - Prob. 21PPSCh. 12.1 - Prob. 22HPCh. 12.1 - Prob. 23HPCh. 12.1 - Prob. 24HPCh. 12.1 - Prob. 25HPCh. 12.1 - Prob. 26HPCh. 12.1 - Prob. 27HPCh. 12.1 - Prob. 28HPCh. 12.1 - Prob. 29STPCh. 12.1 - Prob. 30STPCh. 12.1 - Prob. 31STPCh. 12.1 - Prob. 32STPCh. 12.1 - Prob. 33SRCh. 12.1 - Prob. 34SRCh. 12.1 - Prob. 35SRCh. 12.1 - Prob. 36SRCh. 12.1 - Prob. 37SCh. 12.1 - Prob. 38SCh. 12.1 - Prob. 39SCh. 12.2 - Prob. 1CYPCh. 12.2 - Prob. 2ACYPCh. 12.2 - Prob. 2BCYPCh. 12.2 - Prob. 3CYPCh. 12.2 - Prob. 4CYPCh. 12.2 - Prob. 1CYUCh. 12.2 - Prob. 2CYUCh. 12.2 - Prob. 3CYUCh. 12.2 - Prob. 4CYUCh. 12.2 - Prob. 5PPSCh. 12.2 - Prob. 6PPSCh. 12.2 - Prob. 7PPSCh. 12.2 - Prob. 8PPSCh. 12.2 - Prob. 9PPSCh. 12.2 - Prob. 10PPSCh. 12.2 - Prob. 11PPSCh. 12.2 - Prob. 12PPSCh. 12.2 - Prob. 13PPSCh. 12.2 - Prob. 14PPSCh. 12.2 - Prob. 15PPSCh. 12.2 - Prob. 16PPSCh. 12.2 - Prob. 17PPSCh. 12.2 - Prob. 18PPSCh. 12.2 - Prob. 19PPSCh. 12.2 - Prob. 20PPSCh. 12.2 - Prob. 21PPSCh. 12.2 - Prob. 22PPSCh. 12.2 - Prob. 23PPSCh. 12.2 - Prob. 24PPSCh. 12.2 - Prob. 25PPSCh. 12.2 - Prob. 26PPSCh. 12.2 - Prob. 27PPSCh. 12.2 - Prob. 28HPCh. 12.2 - Prob. 29HPCh. 12.2 - Prob. 30HPCh. 12.2 - Prob. 31HPCh. 12.2 - Prob. 32HPCh. 12.2 - Prob. 33HPCh. 12.2 - Prob. 34STPCh. 12.2 - Prob. 35STPCh. 12.2 - Prob. 36STPCh. 12.2 - Prob. 37STPCh. 12.2 - Prob. 38SRCh. 12.2 - Prob. 39SRCh. 12.2 - Prob. 40SRCh. 12.2 - Prob. 41SRCh. 12.2 - Prob. 42SRCh. 12.2 - Prob. 43SCh. 12.2 - Prob. 44SCh. 12.2 - Prob. 45SCh. 12.3 - Prob. 1ACYPCh. 12.3 - Prob. 1BCYPCh. 12.3 - Prob. 2CYPCh. 12.3 - Prob. 3CYPCh. 12.3 - Prob. 1CYUCh. 12.3 - Prob. 2CYUCh. 12.3 - Prob. 3CYUCh. 12.3 - Prob. 4CYUCh. 12.3 - Prob. 5CYUCh. 12.3 - Prob. 6PPSCh. 12.3 - Prob. 7PPSCh. 12.3 - Prob. 8PPSCh. 12.3 - Prob. 9PPSCh. 12.3 - Prob. 10PPSCh. 12.3 - Prob. 11PPSCh. 12.3 - Prob. 12PPSCh. 12.3 - Prob. 13PPSCh. 12.3 - Prob. 14PPSCh. 12.3 - Prob. 15PPSCh. 12.3 - Prob. 16PPSCh. 12.3 - Prob. 17PPSCh. 12.3 - Prob. 18PPSCh. 12.3 - Prob. 19PPSCh. 12.3 - Prob. 20PPSCh. 12.3 - Prob. 21PPSCh. 12.3 - Prob. 22PPSCh. 12.3 - Prob. 23HPCh. 12.3 - Prob. 24HPCh. 12.3 - Prob. 25HPCh. 12.3 - Prob. 26HPCh. 12.3 - Prob. 27STPCh. 12.3 - Prob. 28STPCh. 12.3 - Prob. 29STPCh. 12.3 - Prob. 30STPCh. 12.3 - Prob. 31SRCh. 12.3 - Prob. 32SRCh. 12.3 - Prob. 33SRCh. 12.3 - Prob. 34SRCh. 12.3 - Prob. 35SRCh. 12.3 - Prob. 36SRCh. 12.3 - Prob. 37SRCh. 12.3 - Prob. 38SRCh. 12.3 - Prob. 39SCh. 12.3 - Prob. 40SCh. 12.3 - Prob. 41SCh. 12.4 - Prob. 1CYPCh. 12.4 - Prob. 2ACYPCh. 12.4 - Prob. 2BCYPCh. 12.4 - Prob. 3CYPCh. 12.4 - Prob. 4CYPCh. 12.4 - Prob. 1CYUCh. 12.4 - Prob. 2CYUCh. 12.4 - Prob. 3CYUCh. 12.4 - Prob. 4CYUCh. 12.4 - Prob. 5CYUCh. 12.4 - Prob. 6PPSCh. 12.4 - Prob. 7PPSCh. 12.4 - Prob. 8PPSCh. 12.4 - Prob. 9PPSCh. 12.4 - Prob. 10PPSCh. 12.4 - Prob. 11PPSCh. 12.4 - Prob. 12PPSCh. 12.4 - Prob. 13PPSCh. 12.4 - Prob. 14PPSCh. 12.4 - Prob. 15PPSCh. 12.4 - Prob. 16PPSCh. 12.4 - Prob. 17PPSCh. 12.4 - Prob. 18PPSCh. 12.4 - Prob. 19PPSCh. 12.4 - Prob. 20PPSCh. 12.4 - Prob. 21PPSCh. 12.4 - Prob. 22PPSCh. 12.4 - Prob. 23PPSCh. 12.4 - Prob. 24PPSCh. 12.4 - Prob. 25PPSCh. 12.4 - Prob. 26HPCh. 12.4 - Prob. 27HPCh. 12.4 - Prob. 28HPCh. 12.4 - Prob. 29HPCh. 12.4 - Prob. 30HPCh. 12.4 - Prob. 31HPCh. 12.4 - Prob. 32STPCh. 12.4 - Prob. 33STPCh. 12.4 - Prob. 34STPCh. 12.4 - Prob. 35STPCh. 12.4 - Prob. 36SRCh. 12.4 - Prob. 37SRCh. 12.4 - Prob. 38SRCh. 12.4 - Prob. 39SRCh. 12.4 - Prob. 40SRCh. 12.4 - Prob. 41SRCh. 12.4 - Prob. 42SCh. 12.4 - Prob. 43SCh. 12.4 - Prob. 44SCh. 12.5 - Prob. 1ACYPCh. 12.5 - Prob. 1BCYPCh. 12.5 - Prob. 2CYPCh. 12.5 - Prob. 1CYUCh. 12.5 - Prob. 2CYUCh. 12.5 - Prob. 3CYUCh. 12.5 - Prob. 4CYUCh. 12.5 - Prob. 5PPSCh. 12.5 - Prob. 6PPSCh. 12.5 - Prob. 7PPSCh. 12.5 - Prob. 8PPSCh. 12.5 - Prob. 9PPSCh. 12.5 - Prob. 10PPSCh. 12.5 - Prob. 11PPSCh. 12.5 - Prob. 12PPSCh. 12.5 - Prob. 13PPSCh. 12.5 - Prob. 14PPSCh. 12.5 - Prob. 15PPSCh. 12.5 - Prob. 16PPSCh. 12.5 - Prob. 17PPSCh. 12.5 - Prob. 18HPCh. 12.5 - Prob. 19HPCh. 12.5 - Prob. 20HPCh. 12.5 - Prob. 21HPCh. 12.5 - Prob. 22HPCh. 12.5 - Prob. 23STPCh. 12.5 - Prob. 24STPCh. 12.5 - Prob. 25STPCh. 12.5 - Prob. 26STPCh. 12.5 - Prob. 27SRCh. 12.5 - Prob. 28SRCh. 12.5 - Prob. 29SRCh. 12.5 - Prob. 30SRCh. 12.5 - Prob. 31SRCh. 12.5 - Prob. 32SRCh. 12.5 - Prob. 33SRCh. 12.5 - Prob. 34SRCh. 12.5 - Prob. 35SCh. 12.5 - Prob. 36SCh. 12.5 - Prob. 37SCh. 12.6 - Prob. 1CYPCh. 12.6 - Prob. 2CYPCh. 12.6 - Prob. 1CYUCh. 12.6 - Prob. 2CYUCh. 12.6 - Prob. 3CYUCh. 12.6 - Prob. 4CYUCh. 12.6 - Prob. 5PPSCh. 12.6 - Prob. 6PPSCh. 12.6 - Prob. 7PPSCh. 12.6 - Prob. 8PPSCh. 12.6 - Prob. 9PPSCh. 12.6 - Prob. 10PPSCh. 12.6 - Prob. 11PPSCh. 12.6 - Prob. 12PPSCh. 12.6 - Prob. 13PPSCh. 12.6 - Prob. 14PPSCh. 12.6 - Prob. 15PPSCh. 12.6 - Prob. 16PPSCh. 12.6 - Prob. 17PPSCh. 12.6 - Prob. 18PPSCh. 12.6 - Prob. 19HPCh. 12.6 - Prob. 20HPCh. 12.6 - Prob. 21HPCh. 12.6 - Prob. 22STPCh. 12.6 - Prob. 23STPCh. 12.6 - Prob. 24STPCh. 12.6 - Prob. 25STPCh. 12.6 - Prob. 26SRCh. 12.6 - Prob. 27SRCh. 12.6 - Prob. 28SRCh. 12.6 - Prob. 29SRCh. 12.6 - Prob. 30SRCh. 12.6 - Prob. 31SRCh. 12.6 - Prob. 32SRCh. 12.6 - Prob. 33SRCh. 12.6 - Prob. 34SRCh. 12.6 - Prob. 35SRCh. 12.6 - Prob. 36SRCh. 12.6 - Prob. 37SRCh. 12.6 - Prob. 38SCh. 12.6 - Prob. 39SCh. 12.6 - Prob. 40SCh. 12.6 - Prob. 41SCh. 12.6 - Prob. 42SCh. 12.6 - Prob. 43SCh. 12.7 - Prob. 1CYPCh. 12.7 - Prob. 2CYPCh. 12.7 - Prob. 3CYPCh. 12.7 - Prob. 1CYUCh. 12.7 - Prob. 2CYUCh. 12.7 - Prob. 3CYUCh. 12.7 - Prob. 4CYUCh. 12.7 - Prob. 5PPSCh. 12.7 - Prob. 6PPSCh. 12.7 - Prob. 7PPSCh. 12.7 - Prob. 8PPSCh. 12.7 - Prob. 9PPSCh. 12.7 - Prob. 10PPSCh. 12.7 - Prob. 11PPSCh. 12.7 - Prob. 12PPSCh. 12.7 - Prob. 13PPSCh. 12.7 - Prob. 14PPSCh. 12.7 - Prob. 15PPSCh. 12.7 - Prob. 16PPSCh. 12.7 - Prob. 17PPSCh. 12.7 - Prob. 18PPSCh. 12.7 - Prob. 19PPSCh. 12.7 - Prob. 20PPSCh. 12.7 - Prob. 21PPSCh. 12.7 - Prob. 22PPSCh. 12.7 - Prob. 23HPCh. 12.7 - Prob. 24HPCh. 12.7 - Prob. 25HPCh. 12.7 - Prob. 26HPCh. 12.7 - Prob. 27STPCh. 12.7 - Prob. 28STPCh. 12.7 - Prob. 29STPCh. 12.7 - Prob. 30STPCh. 12.7 - Prob. 31SRCh. 12.7 - Prob. 32SRCh. 12.7 - Prob. 33SRCh. 12.7 - Prob. 34SRCh. 12.7 - Prob. 35SRCh. 12.7 - Prob. 36SRCh. 12.7 - Prob. 37SCh. 12.7 - Prob. 38SCh. 12.7 - Prob. 39SCh. 12.7 - Prob. 40SCh. 12.7 - Prob. 41SCh. 12.7 - Prob. 42SCh. 12.8 - Prob. 1ACYPCh. 12.8 - Prob. 1BCYPCh. 12.8 - Prob. 2CYPCh. 12.8 - Prob. 3CYPCh. 12.8 - Prob. 4CYPCh. 12.8 - Prob. 1CYUCh. 12.8 - Prob. 2CYUCh. 12.8 - Prob. 3CYUCh. 12.8 - Prob. 4CYUCh. 12.8 - Prob. 5CYUCh. 12.8 - Prob. 6CYUCh. 12.8 - Prob. 7PPSCh. 12.8 - Prob. 8PPSCh. 12.8 - Prob. 9PPSCh. 12.8 - Prob. 10PPSCh. 12.8 - Prob. 11PPSCh. 12.8 - Prob. 12PPSCh. 12.8 - Prob. 13PPSCh. 12.8 - Prob. 14PPSCh. 12.8 - Prob. 15PPSCh. 12.8 - Prob. 16PPSCh. 12.8 - Prob. 17PPSCh. 12.8 - Prob. 18PPSCh. 12.8 - Prob. 19PPSCh. 12.8 - Prob. 20PPSCh. 12.8 - Prob. 21PPSCh. 12.8 - Prob. 22HPCh. 12.8 - Prob. 23HPCh. 12.8 - Prob. 24HPCh. 12.8 - Prob. 25HPCh. 12.8 - Prob. 26HPCh. 12.8 - Prob. 27HPCh. 12.8 - Prob. 28STPCh. 12.8 - Prob. 29STPCh. 12.8 - Prob. 30STPCh. 12.8 - Prob. 31STPCh. 12.8 - Prob. 32SRCh. 12.8 - Prob. 33SRCh. 12.8 - Prob. 34SRCh. 12.8 - Prob. 35SRCh. 12.8 - Prob. 36SCh. 12.8 - Prob. 37SCh. 12.8 - Prob. 38SCh. 12 - Prob. 1QCCh. 12 - Prob. 2QCCh. 12 - Prob. 3QCCh. 12 - Prob. 4QCCh. 12 - Prob. 5QCCh. 12 - Prob. 6QCCh. 12 - Prob. 7QCCh. 12 - Prob. 8QCCh. 12 - Prob. 9QCCh. 12 - Prob. 10QCCh. 12 - Prob. 11QCCh. 12 - Prob. 12QCCh. 12 - Prob. 13QCCh. 12 - Prob. 1MCQCh. 12 - Prob. 2MCQCh. 12 - Prob. 3MCQCh. 12 - Prob. 4MCQCh. 12 - Prob. 5MCQCh. 12 - Prob. 6MCQCh. 12 - Prob. 7MCQCh. 12 - Prob. 8MCQCh. 12 - Prob. 9MCQCh. 12 - Prob. 10MCQCh. 12 - Prob. 11MCQCh. 12 - Prob. 12MCQCh. 12 - Prob. 13MCQCh. 12 - Prob. 14MCQCh. 12 - Prob. 15MCQCh. 12 - Prob. 16MCQCh. 12 - Prob. 1SGRCh. 12 - Prob. 2SGRCh. 12 - Prob. 3SGRCh. 12 - Prob. 4SGRCh. 12 - Prob. 5SGRCh. 12 - Prob. 6SGRCh. 12 - Prob. 7SGRCh. 12 - Prob. 8SGRCh. 12 - Prob. 9SGRCh. 12 - Prob. 10SGRCh. 12 - Prob. 11SGRCh. 12 - Prob. 12SGRCh. 12 - Prob. 13SGRCh. 12 - Prob. 14SGRCh. 12 - Prob. 15SGRCh. 12 - Prob. 16SGRCh. 12 - Prob. 17SGRCh. 12 - Prob. 18SGRCh. 12 - Prob. 19SGRCh. 12 - Prob. 20SGRCh. 12 - Prob. 21SGRCh. 12 - Prob. 22SGRCh. 12 - Prob. 23SGRCh. 12 - Prob. 24SGRCh. 12 - Prob. 25SGRCh. 12 - Prob. 26SGRCh. 12 - Prob. 27SGRCh. 12 - Prob. 28SGRCh. 12 - Prob. 29SGRCh. 12 - Prob. 30SGRCh. 12 - Prob. 31SGRCh. 12 - Prob. 32SGRCh. 12 - Prob. 33SGRCh. 12 - Prob. 34SGRCh. 12 - Prob. 35SGRCh. 12 - Prob. 36SGRCh. 12 - Prob. 37SGRCh. 12 - Prob. 38SGRCh. 12 - Prob. 39SGRCh. 12 - Prob. 40SGRCh. 12 - Prob. 41SGRCh. 12 - Prob. 42SGRCh. 12 - Prob. 1PTCh. 12 - Prob. 2PTCh. 12 - Prob. 3PTCh. 12 - Prob. 4PTCh. 12 - Prob. 5PTCh. 12 - Prob. 6PTCh. 12 - Prob. 7PTCh. 12 - Prob. 8PTCh. 12 - Prob. 9PTCh. 12 - Prob. 10PTCh. 12 - Prob. 11PTCh. 12 - Prob. 12PTCh. 12 - Prob. 13PTCh. 12 - Prob. 14PTCh. 12 - Prob. 15PTCh. 12 - Prob. 16PTCh. 12 - Prob. 17PTCh. 12 - Prob. 18PTCh. 12 - Prob. 1ECh. 12 - Prob. 2ECh. 12 - Prob. 1STPCh. 12 - Prob. 2STPCh. 12 - Prob. 3STPCh. 12 - Prob. 4STPCh. 12 - Prob. 5STPCh. 12 - Prob. 6STPCh. 12 - Prob. 7STPCh. 12 - Prob. 8STPCh. 12 - Prob. 9STPCh. 12 - Prob. 10STPCh. 12 - Prob. 11STPCh. 12 - Prob. 12STPCh. 12 - Prob. 13STP
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