Question

Help with this question, please!!

Answer 1

Answer:

$\boxed{\text{L = 210 ft}^{2} \text{; S = 253.3 ft}^{2}}$

Step-by-step explanation:

Step 1. Lateral area

The lateral area L of the pyramid is the sum of the areas of the three sides.

For one side,

A = ½bh = ½ × 10 × 14 = 70 ft²

L = 3A = 3 × 70 = 210 ft²

Step 2. Base area

The formula for the area B of the triangular base is

B = ½bh

The height of an equilateral triangle is

h = (b√3)/2

So, B = ½b × (b√3)/2 = ¼b²√3

B = ¼ ×10² × √3 = 43.30 ft²

Step 3. Total area

Total surface area = lateral area + base area

S = L + B

S = 210 + 43.30 = 253.3 ft²  

$\boxed{\text{L = 210 ft}^{2} \text{; S = 253.3 ft}^{2}}$