Hello!
Answer:
[tex]\boxed{ \bf The~surface~area~of~the~pyramid~is~348~m^2}[/tex]
_____________________________________________
Explanation:
Step 1: Find the slant height of the face of the triangle. (The hypotenuse is the slant height of the pyramid, so that's what we're looking for.)
We already have one leg (it's 6 cm). The second leg of the triangle is 6 because if you chop the base length in half, you will get the second leg.
Leg 1 = 6
Leg 2 = 6
Now, use this to find the hypotenuse (slant):
S² = 6² + 6²
S² = 36 + 36 = 72
S = 8.49
Next, use the formula for area of a triangle to find the area of all four triangle sides:
a = 1/2 × b × h
a =1/2 × 12 × 8.49
a = 101.88 ÷ 2
a = 50.94
Multiply this number by 4 to get the surface area of all four triangular faces:
50.911686 × 4 = 203.76
Now, find the area of the square base:
a = l × w
a = 12 × 12
a = 144
We're almost done! Finally, add the area of the square base to the area of the four triangles.
144 + 203.76 = 347.76
You can round this to 348.
Have a fabulous day! :)
