How to find the area of a trapezoid - ISEE Lower Level Quantitative Reasoning
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What is the area of a trapezoid if its height is 1, its long base is 4, and its short base is 2?
What is the area of a trapezoid if its height is 1, its long base is 4, and its short base is 2?
The area of a trapezoid is given by the formula 
.
We know that the height is 1, the long base is 4, and the short base is 2.
The area of a trapezoid is given by the formula
We know that the height is 1, the long base is 4, and the short base is 2.
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Which formula would you use to find the area of a trapezoid?
Which formula would you use to find the area of a trapezoid?
The find the area of a trapezoid, use:
The find the area of a trapezoid, use:
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Note: Figure NOT drawn to scale.
Mr. Smith owns the triangular piece of land seen in the above diagram. He sells the trapezoidal parcel shown at bottom right to his brother. What is the area of the land he retains?
Note: Figure NOT drawn to scale.
Mr. Smith owns the triangular piece of land seen in the above diagram. He sells the trapezoidal parcel shown at bottom right to his brother. What is the area of the land he retains?
The area of a triangle is half the product of its base and its height, so Mr. Smith's parcel originally had area
square feet.
The area of a trapezoid is the half product of its height and the sum of its two parallel sides (bases), so the portion Mr. Smith sold to his brother has area
square feet.
Therefore, Mr. Smith retains a parcel of area
square feet.
The area of a triangle is half the product of its base and its height, so Mr. Smith's parcel originally had area
The area of a trapezoid is the half product of its height and the sum of its two parallel sides (bases), so the portion Mr. Smith sold to his brother has area
Therefore, Mr. Smith retains a parcel of area
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The above diagram shows a trapezoidal home within a rectangular yard. What is the area of the yard?
The above diagram shows a trapezoidal home within a rectangular yard. What is the area of the yard?
The area of the yard is the area of the small trapezoid subtracted from that of the large rectangle. The area of a rectangle is the product of its length and its height, so the large rectangle has area
square meters.
The area of a trapezoid is half the product of its height and the sum of its two parallel sides (bases), so the small trapezoid has area
square meters.
The area of the yard is the difference of the two:
square meters.
The area of the yard is the area of the small trapezoid subtracted from that of the large rectangle. The area of a rectangle is the product of its length and its height, so the large rectangle has area
The area of a trapezoid is half the product of its height and the sum of its two parallel sides (bases), so the small trapezoid has area
The area of the yard is the difference of the two:
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What is the area of the above trapezoid?
What is the area of the above trapezoid?
The formula for the area of a trapezoid is 
In other words, find the average of the bases and multiply by the height. Substituting in the values of the bases for the given trapezoid, 
and 
, you get:
The formula for the area of a trapezoid is
In other words, find the average of the bases and multiply by the height. Substituting in the values of the bases for the given trapezoid,
Compare your answer with the correct one above
What is the area of the above trapezoid?
What is the area of the above trapezoid?
The formula for the area of a trapezoid is 
In other words, find the average of the bases and multiply by the height. Substituting the values of the bases of the given trapezoid, 
and 
, into the equation, you get:
The area of the trapezoid is thus 
.
The formula for the area of a trapezoid is
In other words, find the average of the bases and multiply by the height. Substituting the values of the bases of the given trapezoid,
The area of the trapezoid is thus
Compare your answer with the correct one above