Q11. - Geometry

Question

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

$\text{Base\hspace{0.17em}\hspace{0.17em}Area}=\_\_\_$

Step-by-Step Solution

Answer

The base area of the given pyramid is$9\sqrt{3}{\text{\hspace{0.17em}cm}}^2$ .

Step 1. Given information.

The given $V-XYZ$pyramid:

Each edge of pyramid is equal to 6.

Step 2. Determine the value.

The base of the pyramid is triangle XYZ. Each edge of triangle XYZ is 6 and the length of XM is$3\sqrt{3}\text{\hspace{0.17em}\hspace{0.17em}cm}$ .

 

The base area can be calculated as in below.

$\begin{array}{c}A=\frac{1}{2}\times XM\times YZ\\ =\frac{1}{2}\times 3\sqrt{3}\text{\hspace{0.17em}cm}\times 6\text{\hspace{0.17em}cm}\\ =9\sqrt{3}{\text{\hspace{0.17em}cm}}^2\end{array}$

 

Therefore, the base area of the given pyramid is $9\sqrt{3}{\text{\hspace{0.17em}cm}}^2$.