Question
A pastry chef is creating a chocolate does serve in the shape of a triangle. The pyramid has a base of 5 inches. The high base is 4.3 inches and the slight height is 6 inches use the correct formula to find the surface area of the chocolate pyramid One point
Answers
GPT 3.5
The formula to find the surface area of a triangular pyramid is:
Surface Area = Base Area + (Perimeter of Base x Slant Height)/2
To find the base area, we use the formula for the area of a triangle:
Base Area = (1/2) x base x height of base
Base Area = (1/2) x 5 inches x 4.3 inches
Base Area = 10.75 square inches
To find the perimeter of the base, we add the lengths of all three sides:
Perimeter of Base = side 1 + side 2 + side 3
Perimeter of Base = 5 inches + 4.3 inches + 4.3 inches
Perimeter of Base = 13.6 inches
Now, we need to find the slant height. We can use the Pythagorean theorem to find the length of the slant height. The slant height is the hypotenuse of the right triangle formed by the height, half the base, and the slant height.
Using the Pythagorean theorem:
(1/2 x base)^2 + height^2 = slant height^2
(1/2 x 5 inches)^2 + 6 inches^2 = slant height^2
(2.5 inches)^2 + 36 inches^2 = slant height^2
6.25 square inches + 1296 square inches = slant height^2
1302.25 square inches = slant height^2
Now, we take the square root of both sides to find the slant height:
slant height = √1302.25 square inches
slant height ≈ 35.82 inches
Now, we can plug these values into the surface area formula:
Surface Area = 10.75 square inches + (13.6 inches x 35.82 inches)/2
Surface Area ≈ 10.75 square inches + (487.792 inches^2)/2
Surface Area ≈ 10.75 square inches + 243.896 square inches
Surface Area ≈ 254.646 square inches
Therefore, the surface area of the chocolate pyramid is approximately 254.646 square inches.
Surface Area = Base Area + (Perimeter of Base x Slant Height)/2
To find the base area, we use the formula for the area of a triangle:
Base Area = (1/2) x base x height of base
Base Area = (1/2) x 5 inches x 4.3 inches
Base Area = 10.75 square inches
To find the perimeter of the base, we add the lengths of all three sides:
Perimeter of Base = side 1 + side 2 + side 3
Perimeter of Base = 5 inches + 4.3 inches + 4.3 inches
Perimeter of Base = 13.6 inches
Now, we need to find the slant height. We can use the Pythagorean theorem to find the length of the slant height. The slant height is the hypotenuse of the right triangle formed by the height, half the base, and the slant height.
Using the Pythagorean theorem:
(1/2 x base)^2 + height^2 = slant height^2
(1/2 x 5 inches)^2 + 6 inches^2 = slant height^2
(2.5 inches)^2 + 36 inches^2 = slant height^2
6.25 square inches + 1296 square inches = slant height^2
1302.25 square inches = slant height^2
Now, we take the square root of both sides to find the slant height:
slant height = √1302.25 square inches
slant height ≈ 35.82 inches
Now, we can plug these values into the surface area formula:
Surface Area = 10.75 square inches + (13.6 inches x 35.82 inches)/2
Surface Area ≈ 10.75 square inches + (487.792 inches^2)/2
Surface Area ≈ 10.75 square inches + 243.896 square inches
Surface Area ≈ 254.646 square inches
Therefore, the surface area of the chocolate pyramid is approximately 254.646 square inches.