Answer:
Explanation:
To calculate the surface area of a triangular pyramid, we need to find the area of each of its faces and then add them up.
In this case, we know that the base of the pyramid is an equilateral triangle with legs of length 2 yards, so its area can be calculated using the formula for the area of an equilateral triangle:
Area of base = (sqrt(3) / 4) x leg^2
= (sqrt(3) / 4) x 2^2
= sqrt(3)
The slant height of the pyramid is 4 yards, so we can use the Pythagorean theorem to find the height of each triangular face:
Height of each triangular face = sqrt(slant height^2 - (1/2 x leg)^2)
= sqrt(4^2 - (1/2 x 2)^2)
= sqrt(15)
Now we can calculate the area of each triangular face using the formula:
Area of triangular face = (1/2) x base x height
= (1/2) x 2 x sqrt(15)
= sqrt(15)
Therefore, the total surface area of the triangular pyramid is the sum of the areas of its four triangular faces:
Total surface area = 4 x Area of triangular face + Area of base
= 4 x sqrt(15) + sqrt(3)
≈ 20.13 square yards
So, the surface area of the triangular pyramid is approximately 20.13 square yards.