SAT Math : How to find the area of a trapezoid
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Example Question #9 :How To Find The Area Of A Trapezoid
A trapezoid has a base of length 4, another base of lengths, and a height of lengths. A square has sides of lengths. What is the value ofs这样,梯形的面积和面积of the square are equal?
In general, the formula for the area of a trapezoid is (1/2)(a+b)(h), whereaandbare the lengths of the bases, andhis the length of the height. Thus, we can write the area for the trapezoid given in the problem as follows:
area of trapezoid = (1/2)(4 +s)(s)
Similarly, the area of a square with sides of lengthais given bya2. Thus, the area of the square given in the problem iss2.
We now can set the area of the trapezoid equal to the area of the square and solve fors.
(1/2)(4 +s)(s) =s2
Multiply both sides by 2 to eliminate the 1/2.
(4 +s)(s) = 2s2
Distribute theson the left.
4s+s2= 2s2
Subtracts2from both sides.
4s=s2
Becauses必须是一个正数,我们可以分两方面s bys.
4 =s
This means the value ofsmust be 4.
The answer is 4.
Example Question #1 :Quadrilaterals
Find the area of a trapezoid given bases of length 1 and 2 and height of 2.
To solve, simply use the formula for the area of a trapezoid. Thus,
Example Question #2 :Quadrilaterals
The above figure shows Square
If Square
Let
Construct segment
and
The area of Rectangle
The lengths of the legs of Right
and
The area of this right triangle is half the product of these lengths, or
This is seen below:
The sum of these areas is the area of Quadrilateral
Substituting
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