To solve this question you have to calculate the area for each individual triangle that compose the pyramid, notice that the the base of the pyramid is a equilateral triangle with sides of 10 cm, first we have to obtein the height of the base triangle
using the pythagorean theorem we get that
[tex]h\text{ = }\sqrt[]{(10cm)^2-(5cm)^2}^{}\text{ =}\sqrt[]{75}cm[/tex]
Now we use the formula for the area of a triangle A=b*h/2 where b is the base and h is the height, then A= 43.3 cm^2.
Notice that the rest of the triangles have the same base and height b=10cm and h=15cm. So we just have to calculate the area for one of them and multiply by 3. The area in this case is 75cm^2, now we multiply by 3 and get 225cm^2.
Finally we add the areas and get that total area= 225cm^2+43.3cm^2 = 268.3cm^2.
