A net of a triangular pyramid is shown below the base and faces are convergent 4.3 5 what is the surface area in square meters of the pyramid
To find the surface area of a triangular pyramid, we need to find the areas of all its faces and add them together.
First, let's find the area of the base. The base of the pyramid is a triangle, and the area of a triangle can be found using the formula A = 1/2 * base * height.
Given that the base of the triangle is 4.3 meters and one side of the triangle is 5 meters, we need to find the height of the triangle. To do this, we can use the Pythagorean theorem.
Let's call the height of the triangle h. Using the theorem, we have:
(4.3/2)^2 + h^2 = 5^2
(2.15)^2 + h^2 = 25
4.6225 + h^2 = 25
Simplifying:
h^2 = 25 - 4.6225
h^2 = 20.3775
h ≈ √20.3775
h ≈ 4.52 meters
Now we can find the area of the base:
A_base = 1/2 * 4.3 * 4.52
A_base ≈ 9.6586 square meters
Next, let's find the areas of the triangular faces. Each triangular face has the height of the pyramid as its height and one side length of the base triangle as its base.
A_face = 1/2 * 4.3 * 4.52
A_face ≈ 9.6586 square meters
Now, there are 3 triangular faces, so the total area of the triangular faces is:
A_triangular_faces = 3 * A_face
A_triangular_faces ≈ 3 * 9.6586
A_triangular_faces ≈ 28.9758 square meters
Finally, we can find the total surface area by adding the area of the base to the area of the triangular faces:
Total surface area = A_base + A_triangular_faces
Total surface area ≈ 9.6586 + 28.9758
Total surface area ≈ 38.6344 square meters
Therefore, the surface area of the pyramid is approximately 38.6344 square meters.