Find the surface area of a triangular pyramid with b =4 cm, h= 8.2 cm and s = 7 cm. PLEASE. How ?
Lateral surface area
=perimeter of base * apothem /2
=3b*s/2
(for a regular pyramid with a triangular base)
Area of triangular base with side b
=(√3)*b/2*(b/2)
=(√3)b²/4
What is apothem ?
why did you not include the height ?
To find the surface area of a triangular pyramid, you need to know the base length (b), the height (h), and the slant height (s).
Step 1: Calculate the area of the base triangle.
Since you have the base length (b), you can calculate the area of the base triangle using the formula for the area of a triangle:
Area = (base * height) / 2.
In this case, the base length (b) is 4 cm, and the height (h) is not given. As the height of a triangular pyramid is usually different from the slant height, we assume this as the perpendicular height corresponding to the base triangle. Therefore, the area of the base triangle would be:
Area = (4 cm * h) / 2.
Step 2: Find the lateral area.
To find the lateral area, you need to calculate the area of each triangular face and sum them up. The formula for the area of a triangular face is:
Area = (base * slant height) / 2.
For a pyramid, there are four triangular faces, but since two of them share the base triangle, we need to calculate the areas of the other two triangular faces. In this case, the slant height (s) is given as 7 cm, and the base length (b) is still 4 cm. So, the formula becomes:
Area = (4 cm * 7 cm) / 2.
Step 3: Add the base area and lateral area.
To find the total surface area of the triangular pyramid, add the area of the base triangle (calculated in step 1) to the sum of the areas of the other two triangular faces (calculated in step 2). So, the total surface area would be:
Total Surface Area = Area of the base triangle + 2 * Area of the other two triangular faces.
Plug in the values and compute to get the final answer.