We can draw a line perpendicular to the top and bottom lines, which is the height, h
Two right triangles are formed on the ends of the trapezoid.
Since their hypotenuses are equal (5) , and one leg is equal (h) , the other leg must be equal (g) .
Since
g + 6 + g = 14 , we can solve for g .
2g + 6 = 14
2g = 8
g = 4
Now we can solve for h using the Pythagorean theorem.
g2 + h2 = 52
42 + h2 = 52
16 + h2 = 25
h2 = 9 take the + square root of both sides
h = 3
Now we know the height of the trapezoid and the length of both bases.
area of trapezoid = [ (6 + 14)/2 ] * 3
area of trapezoid = [ 10 ] * 3
area of trapezoid = 30 sq. un.
We can draw a line perpendicular to the top and bottom lines, which is the height, h
Two right triangles are formed on the ends of the trapezoid.
Since their hypotenuses are equal (5) , and one leg is equal (h) , the other leg must be equal (g) .
Since
g + 6 + g = 14 , we can solve for g .
2g + 6 = 14
2g = 8
g = 4
Now we can solve for h using the Pythagorean theorem.
g2 + h2 = 52
42 + h2 = 52
16 + h2 = 25
h2 = 9 take the + square root of both sides
h = 3
Now we know the height of the trapezoid and the length of both bases.
area of trapezoid = [ (6 + 14)/2 ] * 3
area of trapezoid = [ 10 ] * 3
area of trapezoid = 30 sq. un.