Answer:
[tex]\boxed{\text{L = 210 ft}^{2} \text{; S = 253.3 ft}^{2}}[/tex]
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
[tex]\boxed{\text{L = 210 ft}^{2} \text{; S = 253.3 ft}^{2}}[/tex]
