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The lengths of the parallel sides of a trapezoid are represented by a and b and it's height by h. The area of the trapezoid can be written as 1/2 ah+1/2 bh. Express this area as the product of two factors.

Sagot :

A=1/2ab+1/2bh each term has 1/2b in common therefor it can be factored out 1/2b(a+b)

The area of the trapezoid as the product of two factors is  [tex]\frac{1}{2} h(a+b)[/tex]  .

                 

What is trapezoid?

A trapezoid is a four-sided closed 2D shape that has an area and a perimeter. It is also called a Trapezium. The sides of a trapezoid are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.  

Area of trapezoid :

A = ½ (a + b) h

where (A) is the area of a trapezoid, 'a' and 'b' are the bases (parallel sides), and 'h' is the height (the perpendicular distance between a and b)

According to the question

The lengths of first parallel side of a trapezoid =  a

The lengths of second parallel side of a trapezoid =  b

The height of a trapezoid = h

and Area of the trapezoid = [tex]\frac{1}{2} ah+\frac{1}{2} bh[/tex]  

Taking common

 Area of the trapezoid =  [tex]\frac{1}{2} h(a+b)[/tex]  

Hence, the area of the trapezoid as the product of two factors is  [tex]\frac{1}{2} h(a+b)[/tex]  .

                                           

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