Show the area of a trapezoid is $A_{T} = \frac{1}{2} (B + b) \times h$ $A_T = 1/2 (B+b)xxh$ where $B = Large base$ $B= "Large base"$ , $b = is small base$ $b= "is small base"$ and $h = altitude$ $h= "altitude"$ ?

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Show the area of a trapezoid is $A_{T} = \frac{1}{2} (B + b) \times h$ $A_T = 1/2 (B+b)xxh$ where $B = Large base$ $B= "Large base"$ , $b = is small base$ $b= "is small base"$ and $h = altitude$ $h= "altitude"$ ?

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Answer 1 · 2016-05-09T08:44:36

Please see below.

Explanation:

Please refer to [Show that the area of a triangle is $A_Delta = 1/2 bxxh$ where b is the base and h the altitude of...](https://socratic.org/questions/show-that-the-area-of-a-triangle-is-a-delta-1-2-bxxh-where-b-is-the-base-and-h-t)

Join $BD$ in the above diagram.

Now area of triangle $ABD$ will be $1/2xxBxxh$

and area of triangle $BCD$ will be $1/2xxbxxh$

Adding the two area of trepezoid $A_T=1/2xxBxxh+1/2xxbxxh$

or = $1/2xx(B+b)xxh$

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Show the area of a trapezoid is $A_{T} = \frac{1}{2} (B + b) \times h$ $A_T = 1/2 (B+b)xxh$ where $B = Large base$ $B= "Large base"$ , $b = is small base$ $b= "is small base"$ and $h = altitude$ $h= "altitude"$ ?

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Show the area of a trapezoid is A_T = 1/2 (B+b)xxhAT=12(B+b)×hA_T = 1/2 (B+b)xxh where B= "Large base"B=Large baseB= "Large base", b= "is small base"b=is small baseb= "is small base" and h= "altitude"h=altitudeh= "altitude"?

1 Answer

Explanation:

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Show the area of a trapezoid is $A_{T} = \frac{1}{2} (B + b) \times h$ $A_T = 1/2 (B+b)xxh$ where $B = Large base$ $B= "Large base"$ , $b = is small base$ $b= "is small base"$ and $h = altitude$ $h= "altitude"$ ?