Q14. - Geometry

Question

Sketch the following square pyramid described. Then find its lateral area, total area, and volume.

$\text{Base} \text{edge}=16, \text{Lateral} \text{edge}=17$

Step-by-Step Solution

Answer

The sketch of the pyramid will be as shown

The lateral area, total area and volume of pyramid are .

Step 1. Given information.

A square pyramid with base edge 16 and lateral edge 17.

Step 2. Sketch the pyramid.

Now to draw pyramid, first draw a parallelogram for the base and sketch diagonals and then draw a vertical segment at the point where the diagonal intersects and then join the vertex to the base vertices,

Thus, the pyramid can be obtained as:

Step 3. Interpretation.

Form the above graph and base edge and lateral edge it can be observed that the lateral area, total area and volume of pyramid are $480,736\text{ and }\frac{256\sqrt{161}}{3}$.