#1**+2 **

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.

g^{2} + h^{2} = 5^{2}

4^{2} + h^{2} = 5^{2}

16 + h^{2} = 25

h^{2} = 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.

hectictar
May 30, 2017

#1**+2 **

Best Answer

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.

g^{2} + h^{2} = 5^{2}

4^{2} + h^{2} = 5^{2}

16 + h^{2} = 25

h^{2} = 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.

hectictar
May 30, 2017