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How to find the Area of the figure without the hieght?

Guest May 30, 2017

Best Answer 

 #1
avatar+5541 
+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.

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.

hectictar  May 30, 2017
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1+0 Answers

 #1
avatar+5541 
+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.

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.

hectictar  May 30, 2017

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