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)
To find the surface area of the pyramid, we need to find the area of the base and the area of the three lateral faces.
The area of the triangular base can be found using the formula for the area of a triangle: (base x height) / 2. In this case, the base is 4.5 cm and the height is 3.9 cm. So, the area of the base is (4.5 cm x 3.9 cm) / 2 = 17.55 cm^2.
The area of each lateral face can be found using the formula for the area of a triangle: (base x height) / 2. In this case, the base is 4.5 cm and the height is 3.5 cm. So, the area of each lateral face is (4.5 cm x 3.5 cm) / 2 = 7.875 cm^2.
Since there are three lateral faces, the total area of the lateral faces is 3 x 7.875 cm^2 = 23.625 cm^2.
The total surface area of the pyramid is the sum of the area of the base and the area of the lateral faces. So, the surface area of the pyramid is 17.55 cm^2 + 23.625 cm^2 = 41.175 cm^2.
Therefore, the surface area of each pyramid is 41.175 cm^2.