Use 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
To find the surface area of the triangular pyramid, we need to find the area of each face and add them together.
The triangular base has a side length of 4.5 cm and a height of 3.9 cm. The area of a triangle is given by the formula A = (1/2) * base * height. Plugging in the values we have, the area of the triangular base is (1/2) * 4.5 cm * 3.9 cm = 8.775 cm^2.
Next, we need to find the area of the three triangular faces. Each face is a right triangle with a base of 4.5 cm and a height of 3.5 cm. The area of each face is (1/2) * 4.5 cm * 3.5 cm = 7.875 cm^2.
Finally, we add up the areas of the base and the three faces: 8.775 cm^2 + 7.875 cm^2 + 7.875 cm^2 + 7.875 cm^2 = 32.4 cm^2.
Therefore, the surface area of each pyramid is 32.4 cm^2.