PSAT Math aid » Geometry » aircraft Geometry » square » Trapezoids » how to discover the area the a trapezoid

A trapezoid has actually a basic of length 4, another base of size s, and also a height of length s. A square has sides of size s. What is the value of s such the the area the the trapezoid and also the area the the square are equal?


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Explanation:

In general, the formula because that the area that a trapezoid is (1/2)(a + b)(h), whereby a and also b are the lengths the the bases, and also h is the size of the height. Thus, we can write the area because that the trapezoid provided in the problem as follows:

area of trapezoid = (1/2)(4 + s)(s)

Similarly, the area of a square with sides of size a is given by a2. Thus, the area of the square given in the problem is s2.

You are watching: What is the area of the trapezoid the diagram is not drawn to scale

We now can collection the area that the trapezoid equal to the area of the square and also solve for s.

(1/2)(4 + s)(s) = s2

Multiply both sides by 2 to remove the 1/2.

(4 + s)(s) = 2s2

Distribute the s ~ above the left.

4s + s2 = 2s2

Subtract s2 indigenous both sides.

4s = s2

Because s have to be a positive number, we have the right to divide both political parties by s.

4 = s

This method the value of s have to be 4.

The price is 4.


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Example concern #284 : aircraft Geometry


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Note: number NOT drawn to scale.


The white an ar in the over diagram is a trapezoid. What percent the the above rectangle, rounded to the nearest totality percent, is blue?


Possible Answers:
Correct answer:

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Explanation:

The area the the entire rectangle is the product that its length and width, or

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.

The area of the white trapezoid is one half the product that its height and also the sum of its basic lengths, or 

*

Therefore, the blue polygon has actually area 

*

This is 

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 of the rectangle.

Rounded, this is 70%.


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Example concern #285 : airplane Geometry


Refer come the over diagram. 

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.

Give the area the Quadrilateral 

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.


Possible Answers:
Correct answer:

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Explanation:

 

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, because both space right; by the equivalent Angles Theorem,
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, and Quadrilateral 
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 is a trapezoid.

 

By the Angle-Angle Similarity Postulate, since 

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and

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 (by reflexivity),

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and due to the fact that corresponding political parties of similar triangles are in proportion,

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*

*

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, the bigger base of the trapozoid;

The smaller sized base is 

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.

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, the elevation of the trapezoid.

The area that the trapezoid is 

*

*

*


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