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.
cm2
please round
To find the surface area of a triangular pyramid, we need to calculate the area of the triangular base and add it to the sum of the areas of the three triangular faces.
The triangular base has a side length of 4.5 cm and a perpendicular height of 3.9 cm. Using the formula for the area of a triangle, the area of the base is (1/2) x base x height = (1/2) x 4.5 cm x 3.9 cm = 8.775 cm^2.
The area of each triangular face can be calculated using the formula (1/2) x base x height. Each face has a base length equal to the side length of the base (4.5 cm) and a height equal to the perpendicular height from the apex to the center of the base (3.5 cm). So, the area of each triangular face is (1/2) x 4.5 cm x 3.5 cm = 7.875 cm^2.
Since there are three triangular faces, we need to multiply this value by 3 to calculate the total area of the three faces.
Adding the area of the base to the area of the three faces, the surface area of the pyramid is 8.775 cm^2 + 3 x 7.875 cm^2 = 41.175 cm^2.
Rounding to the nearest whole number, the surface area of each pyramid is approximately 41 cm^2.