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

Answer 1

Base area = 1/2·4.5·3.9 = 8.775 cm^2.

Distance from center to midpoint of a side = (3√3)/4 ≈ 1.299 cm.
Slant height = sqrt(3.5^2 + 1.299^2) = sqrt(13.9375) ≈ 3.733 cm.

Lateral area = 3·(1/2·4.5·3.733) = 6.75·3.733 ≈ 25.200 cm^2.

Total surface area ≈ 8.775 + 25.200 = 33.975 ≈ 34.0 cm^2.

Answer: 34.0 cm^2 (approximately).