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Zorluk: OrtaPerimeter and Area of 2D Figures

A municipal park features a garden in the shape of a trapezoid. The parallel sides of the garden measure 1818 meters and 1212 meters. If the total area of the garden is 150150 square meters, what is the perpendicular distance between the parallel sides?

  1. A
    55 meters
  2. 1010 metersCevap
  3. C
    3030 meters
  4. D
    5050 meters

Cevap

The perpendicular distance between the parallel sides is 1010 meters.
The correct answer accurately applies the trapezoid area formula. By setting 150=12(18+12)h150 = \frac{1}{2}(18 + 12)h, the sum of the bases is calculated as 3030. Multiplying by 12\frac{1}{2} results in 1515. Dividing the total area (150150) by 1515 yields a perpendicular height of 1010 meters.

Adım Adım Çözüm

1
Identify the formula for the area of a trapezoid.
A=12(b1+b2)hA = \frac{1}{2}(b_1 + b_2)h
This formula relates the known area and bases to the unknown height.
2
Substitute the known values into the formula.
150=12(18+12)h150 = \frac{1}{2}(18 + 12)h
The given area is 150150, and the bases are 1818 and 1212.
3
Simplify the sum inside the parentheses.
150=12(30)h150 = \frac{1}{2}(30)h
Adding the lengths of the bases gives 3030.
4
Multiply 3030 by 12\frac{1}{2}.
150=15h150 = 15h
This isolates the variable term hh.
5
Divide both sides by 1515 to solve for hh.
h=10h = 10
Dividing by 1515 determines the perpendicular height.

Anahtar Kavram

Using the area formula of a trapezoid to solve for an unknown dimension.
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Konular

Perimeter and Area of 2D Figures

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