Question

Find the lateral area of the square pyramid shown to the nearest whole number.

25 yd
A
43 yd

Answer 1

The lateral surface area of the square pyramid o the nearest whole number is: 2836 yd²

What is the lateral surface area of the square pyramid?

The formula for the lateral surface area of the square pyramid is expressed as:

LSA = a√(a² + 4h²)

Where:

a is length of base

h s perpendicular height

From the diagram, we see that:

a = 43 yd

h = 25 yd

Thus:

LSA = 43√(43² + 4(25)²)

LSA = 2835.72 yd²

Approximating to to the nearest whole number gives:

LSA = 2836 yd²

Answer 2

4,300

Explanation:

Lateral area of a squared Pyramid is given as ½ × Perimeter of base (P) × slant height of pyramid

Thus, we are given,

Side base length (s) = 43 yd

height (h) = 25 yd

Let's find the perimeter

Permimeter = 4(s) = 4(43) = 172 yd

Calculate the slant height using Pythagorean theorem.

Thus, l² = s²+h²

l² = 43²+25² = 1,849+625

l² = 2,474

l = √2,474

l ≈ 50 yd

=>Lateral area = ½ × 172 × 50

= 172 × 25

= 4,300 yd