Chapter 12: Q5. (page 484)

V- ABCD is a regular square pyramid. Find the following numerical answers.
$L.A. =___$

Short Answer

Expert verified

The lateral area of the pyramid is $240 {unit}^{2}$ .

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.

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

Now, calculate the lateral surface area.

$\begin{matrix} LateralSurfaceareaofpyramid = 4 \times areaofone-triangularface \\ LateralSurfaceareaofpyramid = 4 \times 60 \\ = 240 {unit}^{2} \end{matrix}$

Therefore, the lateral surface area of pyramid shown in figur $240 {unit}^{2}$ e is

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V- ABCD is a regular square pyramid. Find the following numerical answers.
$L.A. =___$

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.L.A.=___

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

Logic and Functions

Geometry

Statistics

Applied Mathematics

Discrete Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

V- ABCD is a regular square pyramid. Find the following numerical answers.
$L.A. =___$