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中文版解题过程已知S阴影

=20 \mathrm{~m}^{2}

，EF为中位线。求梯形

A B C D

的面积。

Aug 4, 2024

中文版解题过程

Solution by Steps

step 1

Given that the area of the shaded region is

20 \, \mathrm{m}^2

and EF is the midline of triangle AEF

step 2

Since EF is the midline, it divides triangle AEF into two smaller triangles of equal area

step 3

The area of triangle AEF is twice the area of the shaded region, so

S_{\triangle AEF} = 2 \times 20 \, \mathrm{m}^2 = 40 \, \mathrm{m}^2

step 4

The area of parallelogram CDFB is twice the area of triangle AEF, so

S_{\text{parallelogram}} = 2 \times 40 \, \mathrm{m}^2 = 80 \, \mathrm{m}^2

step 5

The area of trapezoid ABCD is the same as the area of parallelogram CDFB, so

S_{\text{trapezoid}} = 80 \, \mathrm{m}^2

Answer

The area of trapezoid ABCD is

80 \, \mathrm{m}^2

Key Concept

Area calculation using midline properties

Explanation

The midline of a triangle divides it into two smaller triangles of equal area, which helps in calculating the area of the larger shapes.