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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 12: Q4. (page 484)

V- ABCD is a regular square pyramid. Find the following numerical answers.
$A r e a 鈥夆赌� o f 鈥夆赌� 螖 V B C =___$

Short Answer

Expert verified

The area of $螖 V B C$ is $60 {unit}^{2}$ .

Step by step solution

01

Step 1. Given information.

The given $V 鈭� A B C D$ is a regular square pyramid.

Also, $A B = 12$ and $B C = 12$ .

02

Step 2. Determine the value.

The edge length of square base is 12 and height of pyramid is 8.

The length of OMcan be calculated as:

$\begin{matrix} O M = \frac{1}{2} A B \\ = \frac{1}{2} (12) \\ = 6 \end{matrix}$

In $螖 V O M$ , apply Pythagoras Theorem to calculate the slant height.

$\begin{matrix} {(V O)}^{2} + {(O M)}^{2} = {(V M)}^{2} \\ 8^{2} + 6^{2} = l {}^{2} \\ l^{2} = 64 + 36 \\ l^{2} = 100 \end{matrix}$

Further simplify.

$\begin{matrix} l = \sqrt{100} \\ = 卤 10 \end{matrix}$

The height cannot be negative. Neglect the negative value of l.

Therefore, the value of the slant height l is 10 unit.

03

Step 3. Determine the area.

In $螖 V B C$ , calculate the area.

$\begin{matrix} Area (螖 V B C) = \frac{1}{2} 脳 base 脳 height \\ = \frac{1}{2} 脳 (12) 脳 (10) \\ = 6 脳 10 \\ = 60 {unit}^{2} \end{matrix}$

Therefore, the area of $螖 V B C$ from the given figure is $60 {unit}^{2}$

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Most popular questions from this chapter

Refer to rectangular solids with dimensions l, w and h. Complete the following table.

$\begin{matrix} l & 5 x \\ w & 4 x \\ h & 3 x \\ L.A. \\ T.A. \\ V \end{matrix}$

V- ABCD is a regular square pyramid. Find the following numerical answers.

$V C =___$

How many lateral faces are in the following prism?

Refer to cubes with edges of length e. Complete the following table.

$\begin{matrix} e & 2 x \\ T . A . \\ V \end{matrix}$

A right prism has height h and bases that are regular hexagons with sides s. Show that the volume is $\frac{3}{2} s^{2} h \sqrt{3}$ .

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