Surface Area of a Triangular Pyramid
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Here is a triangular pyramid and its net. The lateral faces are congruent triangles. The base (shaded) is an equilateral triangle. (All lengths are in feet.) (a) Find the area of the base of the pyramid. [ ] ft^2 (b) Find the area of one lateral face of the pyramid. [ ] ft^2 (c) Use the net to find the lateral surface area of the pyramid. The base is not included. [ ] ft^2 (d) Use the net to find the total surface area of the pyramid. [ ] ft^2
This question includes visual content: The image shows a 3D sketch of a triangular pyramid at the top left, and below it, its 2D net. The net consists of an equilateral triangle (base) surrounded by three congruent triangles. The height of each lateral triangle is marked as 5, the base side length of the equilateral base is marked as 8, and the altitude/height of the base triangle is marked as 6.9.
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Step by Step Written Solution
Hi Logan, let's solve this problem involving the surface area of a triangular pyramid by examining its net.
Triangular Pyramid Analysis
First, for part a, we need to find the area of the base. The problem states the base is an equilateral triangle. Looking at the net, the shaded base has a side length of eight and a height of six point nine.
Let's plug in those values: base equals eight and height equals six point nine.
Calculating this gives us twenty-seven point six square feet. This is the area of the shaded central triangle.
Next, let's find the area of one lateral face for part b. These are the three outer triangles in the net.
Lateral Face Area
Each lateral face has a base of eight and a height, or slant height, of five, as indicated on the top triangle of the net.
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