se the image to answer the question.
An illustration shows a 3 D triangular prism. The side of the base is 4.5 centimeters. The perpendicular height of the triangular base is 3.9 centimeters. The perpendicular height of the lateral face from the apex to the center of the base is 3.5 centimeters. There are two right angle symbols to show the perpendicular lines. The heights are shown as dashed lines.
A metalworker is creating decorative points in the form of triangular pyramids to go on top of a fence she is building. She wants to know the surface area of each pyramid. Use the surface area formula to find the surface area of each pyramid based on the figure.
(1 point)
cm2
The surface area formula for a triangular pyramid is given by:
Surface Area = base area + (perimeter of base * slant height)/2
In this case, the base of the triangular pyramid is a triangle with base length 4.5 cm and height 3.9 cm. Thus, the base area can be calculated as:
Base Area = (1/2) * base length * height
= (1/2) * 4.5 cm * 3.9 cm
= 8.775 cm^2
The perimeter of the base can be calculated as the sum of the lengths of all three sides of the triangle. Since it is an equilateral triangle, all three sides are equal to 4.5 cm. Thus, the perimeter of the base is:
Perimeter of Base = 3 * side length
= 3 * 4.5 cm
= 13.5 cm
Finally, the slant height of the pyramid is given as 3.5 cm.
Plugging these values into the surface area formula:
Surface Area = 8.775 cm^2 + (13.5 cm * 3.5 cm)/2
= 8.775 cm^2 + 47.25 cm^2/2
= 8.775 cm^2 + 23.625 cm^2
= 32.4 cm^2
Therefore, the surface area of each pyramid is 32.4 cm^2.