2. The faces of a triangular pyramid have a base of 5 cm and a height of 11 cm . What is the lateral area of the pyramid?

Question

UpStudy AI · Accepted Answer

Let the area of one lateral triangular face be calculated using the formula for the area of a triangle:

$$
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
$$

Given that for each lateral face the base is $$5 \, \text{cm}$$ and the height is $$11 \, \text{cm}$$, the area of one lateral face is:

$$
\text{Area of one face} = \frac{1}{2} \times 5 \times 11 = \frac{55}{2} \, \text{cm}^2
$$

Since a triangular pyramid has $$3$$ lateral faces, the total lateral area $$A$$ is:

$$
A = 3 \times \frac{55}{2} = \frac{165}{2} \, \text{cm}^2
$$

Thus, the lateral area of the pyramid is:

$$
\frac{165}{2} \, \text{cm}^2 \,\,\, \text{or} \,\,\, 82.5 \, \text{cm}^2
$$
The lateral area of the pyramid is $$82.5 \, \text{cm}^2$$.

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