Question

HELP NEEDED!! FIND THE AREA OF THE TRAPEZOID!! EXPLAIN !! BOGUS ANSWERS REPORTED

Answer 1

area of trapezoid = (1/2)(B + b)h

where B = length of one base; b = length of the other base; h = height

You have

b = 12 ft (the upper base)

B = 8.7 ft + 12 ft = 20.7 ft (the lower base)

Now we need the height, h. The triangle has a right angle and a 30-deg angle, so the third angle must measure 60 deg. It is a 30-60-90 triangle. In a 30-60-90 triangle, the hypotenuse is trwice the length of the shourt leg. The height of the trapezoid is the short leg of the triangle.

h = (10 ft) /2 = 5 ft

The height of the trapezoid is 5 ft.

area of trapezoid = (1/2)(20.7 + 12)(5) ft^2

area = 81.75 ft^2

Answer: 81.75

Answer 2

we know that Area of a trapezoid $=1/2(a+b)*h$

$a$ and $b$ are parallel sides

$h$ is the height or altitude of the trapezoid

we have $a=8.7+12=20.7 ft$

$b=12 ft$.

we need to find $h$ by using pythagorean identity.

$(hypotensue)^2=(base)^2+(altitude)^2$

$altitude=\sqrt{(hypotensue)^2-(base)^2}$

$altitude=h=\sqrt{(10)^2-(8.7)^2} =4.93ft$

area of the trapezoid $=1/2(20.7+12)*4.93=80.61ft^2$