Multiple Choice Question (MCQ)

In the figure, the area of quadrilateral ABCD is

  1. ×

    32

  2. ×

    33

  3. ×

    34

  4. ×

    35

  5. 36

Collected in the board: Triangle

Steven Zheng posted 3 months ago


Answer

  1. Since \triangle ABD is a right triangle,


    BD = \sqrt{3^2+4^2} =5


    \because 13^2 = 12^2+5^2 =169


    The measure of three sides of \triangle BCD has the following relationship

    BC^2 = BD^2+CD^2

    Therefore, \triangle BCD is also a right triangle.


    So the area of quadrilateral ABCD is,

    A_{ABCD} =A_{\triangle ABD }+A_{\triangle BCD }

    =\dfrac{1}{2}\cdotp 3\cdotp 4+\dfrac{1}{2}\cdotp 5\cdotp 12

    =36

Steven Zheng posted 3 months ago

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