Question

can someone please help me find the surface area of the pyramid with an equilateral triangle for a base

Answer 1

To obtain the total surface we have to calculate the surface of the 4 triangles and add up the areas (remember that the area of a triangle is (b*h)/2 , b is the base, h is the height ).

We will caculate first the area of the base triangle for that we considerer the fact that it is an equilateral triangle with sides of lenght 6 cm, now we calculate the height, I am going to draw please wait a moment

using the pythagorean theorem we have that

$\begin{gathered} h^2=6^2cm^2-3^2\operatorname{cm}=27cm^2 \\ h=\text{ }\sqrt[]{27\text{ }}cm \end{gathered}$

Then, the area of the triangle is 6*h/2 = 3h = 15.59 cm^2.

Now we calculate the area of the other 3 triangles, notice that those triangles have the same base and height so we will calculate for one of them and multiply by 3. From the image we know that the height is 15cm and the base is 6 cm so the area is 45cm^2, and 45*3 cm^2 = 135cm^2.

Finally we add up all the areas:

$135cm^2+15.59cm^2=150.59cm^2$