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Question

Which of the following is true about the above quadrilateral?
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A
Area of quadrilateral can be calculated by one general formula of area of triangle
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B
Area of quadrilateral cannot be calculate by the general formula of area of triangle because of the absence of height
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C
Height is AD and BC in ADC and ABC respectively.
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D
Area of Quadrilateral can be easily calculated by the heron's formula.
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Solution

The correct options are
A Area of quadrilateral cannot be calculate by the general formula of area of triangle because of the absence of height
C Area of Quadrilateral can be easily calculated by the heron's formula.
If ABCD is a quadrilateral, AB=3 cm, AD=5 cm, BC=4 cm and CD=4 cm and AC=5 cm.

Area of ABCD= Area of triangle ACD+Area of triangle ACB

In ACD,

S=5+5+42=142=7 cm

Now area of ACD is:

A=s(sa)(sb)(sc)=7(75)(75)(74)=7×2×2×3=84=221 cm2

In ACB,

S=3+4+52=122=6 cm

Now area of ACB is:

A=s(sa)(sb)(sc)=6(63)(64)(65)=6×3×2×1=36=6 cm2

Hence, area of quadrilateral ABCD is (6+221) cm2.

Area of quadrilateral ABCD cannot be found by the general formula of area of triangle because the height is not given.

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