PSAT数学:如何找到一个陷阱ezoid
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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 ofssuch that the area of the trapezoid and the area 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
Becausesmust be a positive number, we can divide both sides bys.
4 =s
This means the value ofsmust be 4.
The answer is 4.
Example Question #1 :Trapezoids
Note: Figure NOT drawn to scale.
The white region in the above diagram is a trapezoid. What percent of the above rectangle, rounded to the nearest whole percent, is blue?
The area of the entire rectangle is the product of its length and width, or
The area of the white trapezoid is one half the product of its height and the sum of its base lengths, or
Therefore, the blue polygon has area
This is
Rounded, this is 70%.
Example Question #2 :How To Find The Area Of A Trapezoid
Refer to the above diagram.
Give the area of Quadrilateral
By the Angle-Angle Similarity Postulate, since
and
and since corresponding sides of similar triangles are in proportion,
The smaller base is
The area of the trapezoid is
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