Chapter 12: Q15. (page 484)

Each edge of pyramid V- XYZ is 6 cm. Find the following numerical answers.
$T.A. =___$

Short Answer

Expert verified

The total area of the pyramid $V - X Y Z$ is equal to $36 \sqrt{3} {cm}^{2}$ .

Step by step solution

Step 1. Given information.

The given $V - X Y Z$ pyramid:

Each edge of pyramid is equal to 6.

Step 2. Write the concept.

The total area of the pyramid is the sum of lateral area and area of base and the area of each face is equal to the area of the base.

$T.A. = (n + 1) (B)$

The area of each face is equal to the area of the base.

The base of the pyramid is equilateral triangle with edge of triangle is equal to 6 cm.

The formula for the area of the equilateral triangle is,

$B = \frac{\sqrt{3}}{4} a^{2}$

Step 3. Determine the Lateral Area.

Substitute 6 for a in the formula for area.

$\begin{matrix} B = \frac{\sqrt{3}}{4} a^{2} \\ = \frac{\sqrt{3}}{4} {(6)}^{2} \\ = \frac{\sqrt{3}}{4} (36) \\ = 9 \sqrt{3} \end{matrix}$

Substitute $9 \sqrt{3}$ for B and 3 for n in the formula for lateral area.

$\begin{matrix} T.A. = (n + 1) (B) \\ = 4 (9 \sqrt{3}) \\ = 36 \sqrt{3} \end{matrix}$

Therefore, the total area of the pyramid $V - X Y Z$ is equal to $36 \sqrt{3} {cm}^{2}$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Each edge of pyramid V- XYZ is 6 cm. Find the following numerical answers.
$T.A. =___$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the concept.

Step 3. Determine the Lateral Area.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Logic and Functions

Decision Maths

Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Each edge of pyramid V- XYZ is 6 cm. Find the following numerical answers.T.A.=___

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the concept.

Step 3. Determine the Lateral Area.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Logic and Functions

Decision Maths

Applied Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Each edge of pyramid V- XYZ is 6 cm. Find the following numerical answers.
$T.A. =___$