Calculate the surface area of the triangular pyramid.

Question

its a triangle and in the inside of the triangle has an upside down triangle and it says 3 cm and outside the upside down and big triangle shows 3 of 3 cm

Answer 1

To calculate the surface area of the triangular pyramid, we first need to find the area of the base and the lateral faces.

The base of the pyramid is a triangle with sides of length 3 cm. Since it is equilateral, we can use the formula for the area of an equilateral triangle:

Area of the base = (sqrt(3)/4) * s^2, where s is the side length
Area of the base = (sqrt(3)/4) * 3^2 = (sqrt(3)/4) * 9 = (9sqrt(3))/4 ≈ 3.897 cm^2

Next, we need to find the area of the three lateral faces. The lateral faces are triangles with a base of 3 cm and a height of 3 cm. Since there are three lateral faces, we multiply this area by 3:

Area of each lateral face = (1/2) * base * height = (1/2) * 3 * 3 = 4.5 cm^2
Total area of all three lateral faces = 4.5 * 3 = 13.5 cm^2

Finally, we calculate the total surface area of the pyramid by adding the area of the base and the lateral faces:

Surface area = Area of base + Area of lateral faces
Surface area = 3.897 + 13.5 = 17.397 cm^2

Therefore, the surface area of the triangular pyramid is approximately 17.397 cm^2.