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
The surface area of a triangular pyramid can be found using the formula:
Surface Area = Area of Base + Area of Lateral Faces
The base of the pyramid is a triangle, so we can find the area of the base by using the formula for the area of a triangle:
Area of Base = (1/2) * base * height
In this case, the base of the triangular prism is 4.5 cm and the perpendicular height of the base is 3.9 cm. Plugging these values into the formula:
Area of Base = (1/2) * 4.5 cm * 3.9 cm
= 8.775 cm^2
Next, we need to find the area of the lateral faces. The lateral face is a triangle with a base of the same length as the base of the pyramid (4.5 cm). The height of the lateral face is given as 3.5 cm. Again, using the formula for the area of a triangle:
Area of Lateral Face = (1/2) * base * height
= (1/2) * 4.5 cm * 3.5 cm
= 7.875 cm^2
Finally, we can add the areas of the base and the lateral face to find the total surface area:
Surface Area = Area of Base + Area of Lateral Faces
= 8.775 cm^2 + 7.875 cm^2
= 16.65 cm^2
Therefore, the surface area of each pyramid is 16.65 cm^2.