Question

Please help me out please

Answer 1

A = 64√2 ft² = approx. 90.5 ft²

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

Answer 2

110.9 sq ft

Explanation:

split the equilateral triangle into two right triangles. use pythagorean theorem to discover that the height is about 13.86 ft. use the area formula, A= (1/2)bh

A=(1/2)(8)(13.86)= 110.9