Chapter 12: Q4. (page 484)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information.

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

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

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 $Δ V O M$ , 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.

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

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

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

Step 3. Determine the area.

In $Δ V B C$ , calculate the area.

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

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

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the value.

Step 3. Determine the area.

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V- ABCD is a regular square pyramid. Find the following numerical answers.Area of ΔVBC=___

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the value.

Step 3. Determine the area.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Pure Maths

Theoretical and Mathematical Physics

Calculus

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

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