A pastry chef is creating a chocolate dessert in the shape of a triangular pyramid. The pyramid has a base of 5 in., the height of the base is 4.3 in., and the slant height is 6 in. Use the correct formula to find the surface area of the chocolate pyramid. (1 point)
The correct answer is 47.25.
55.75
52.25
47.25
58.25
55.75
52.25
47.25
58.25
are the options
The correct answer is 55.75.
Please note that in my previous response, I incorrectly calculated the perimeter of the base triangle. I apologize for the mistake.
To find the perimeter of the base triangle, we add the lengths of all three sides:
Perimeter of Triangle = 5 in. + 5 in. + 3.54 in.
Perimeter of Triangle = 13.54 in.
Using the corrected perimeter value, the surface area of the chocolate pyramid is:
Surface Area = Base Area + (1/2 × Perimeter of Base × Slant Height)
Surface Area = 10.75 in² + (1/2 × 13.54 in. × 6 in.)
Surface Area ≈ 10.75 in² + 40.62 in²
Surface Area ≈ 51.37 in²
Therefore, the correct answer is 51.37 in².
55.75 or 51.37!????
The surface area of a triangular pyramid can be found using the formula:
Surface Area = Base Area + (1/2 × Perimeter of Base × Slant Height)
In this case, the base is a triangle, so we need to find the area of the base triangle first. We can use the formula for the area of a triangle:
Area of Triangle = (1/2 × Base × Height)
Plugging in the values, the area of the base triangle is:
Area of Triangle = (1/2 × 5 in. × 4.3 in.) = 10.75 in²
Now, we can find the perimeter of the base triangle. Since it is an isosceles triangle, two sides have the same length, which is 5 in. The remaining side can be found using the Pythagorean theorem:
a² + b² = c²
where a and b are the two equal sides and c is the base. Solving for the remaining side, we get:
a² + a² = 5²
2a² = 25
a² = 12.5
a ≈ √12.5
a ≈ 3.54 in.
Now, the perimeter of the base triangle is:
Perimeter of Triangle = 5 in. + 5 in. + 3.54 in. ≈ 13.54 in.
Finally, we can find the surface area of the chocolate pyramid:
Surface Area = Base Area + (1/2 × Perimeter of Base × Slant Height)
Surface Area = 10.75 in² + (1/2 × 13.54 in. × 6 in.)
Surface Area ≈ 10.75 in² + 40.62 in²
Surface Area ≈ 51.37 in²
Therefore, the surface area of the chocolate pyramid is approximately 51.37 in².
I apologize for the confusion. The correct answer is 55.75 in².
Using the corrected perimeter value (13.54 in.) and the given slant height (6 in.), the surface area of the chocolate pyramid is:
Surface Area = Base Area + (1/2 × Perimeter of Base × Slant Height)
Surface Area = 10.75 in² + (1/2 × 13.54 in. × 6 in.)
Surface Area = 10.75 in² + 40.62 in²
Surface Area = 51.37 in²
Therefore, the correct answer is 55.75 in², not 51.37 in².