Answer:
A = 64√2 ft² = approx. 90.5 ft²
Step-by-step explanation:
Because this is an equilateral triangle, the interior angles are also equal and are 60° each. We'll use the area-of-a-triangle formula, A = (1/2)(b)(h), to find the area of this particular triangle. We see from the diagram that the base is 16 ft.
Drawing an imaginary line representing the height of this triangle, and letting h represent this height, we get
sin 60° = opp / hyp = h / (16 ft) = 1/√2, so that
h 1
----- = -----
16 √2 16
and so √2*h = 16, and h = -------
√2
1 16 16
Then the area of this blue triangle is A = (1/2)(b)(h) = ---- * ----- * -------
2 1 √2
128 128√2
or A = ------- = ------------ = 64√2 ft² = approx. 90.5 ft²
√2 2
