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Question
Eric buys a trapezoid field near a river to grow maize. The two parallel sides of the field, AB and CD, are of lengths 50 yards and 110 yards, respectively, and the height (h) is 50 yards.
If CE = DF, find the area in which Eric can grow maize.
Eric buys a trapezoid field near a river to grow maize. The two parallel sides of the field, AB and CD, are of lengths 50 yards and 110 yards, respectively, and the height (h) is 50 yards.
If CE = DF, find the area in which Eric can grow maize.
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Solution
The correct option is A 4000 square yards
Length of AB = 50 yards
AB is parallel to CD.
In CD,
Length of CD = 110 yards
Length of EF = 50 yards
CE = FD
We observe, CD = CE + EF + FD
Substituting the values, we get:
110 yards = 2CE + 50 yards
⇒ 60 yards = 2CE
⇒ 30 yards = CE
As CE = FD, CE = FD = 30 yards
To find the area, we can overlap △BEC above △AFD.
Now, let us rename the points and analyze the lengths obtained.
Thus, a rectangle is formed with a length of 80 yards and a width (h) of 50 yards.
Thus, the area of the field will be:
Area of rectangle = Length × Width
i.e., Area of rectangle = 80 × 50 = 4000 square yards
Thus, the area of the field in which Eric can grow maize is 4000 square yards.
Length of AB = 50 yards
AB is parallel to CD.
In CD,
Length of CD = 110 yards
Length of EF = 50 yards
CE = FD
We observe, CD = CE + EF + FD
Substituting the values, we get:
110 yards = 2CE + 50 yards
⇒ 60 yards = 2CE
⇒ 30 yards = CE
As CE = FD, CE = FD = 30 yards
To find the area, we can overlap △BEC above △AFD.
Now, let us rename the points and analyze the lengths obtained.
Thus, a rectangle is formed with a length of 80 yards and a width (h) of 50 yards.
Thus, the area of the field will be:
Area of rectangle = Length × Width
i.e., Area of rectangle = 80 × 50 = 4000 square yards
Thus, the area of the field in which Eric can grow maize is 4000 square yards.
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