Find the area of a quadrilateral whose sides are 8 cm, 15 cm, 16 cm and 17 cm and the angle between first two sides is a right angle.


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Answer:

180 cm2

Step by Step Explanation:
  1. Let's ABCD is the quadrilateral with AB = 8 cm, BC = 15 cm, CD = 16 cm, DA = 17 cm, and angle ∠ABC = 90°, as shown in the following figure.
  2. Let's draw the diagonal AC in the quadrilateral ABCD,

    The area of the right triangle ABC =  
    1
    2
      × AB × BC
    =  
    1
    2
      × 8 × 15
    = 60 cm2.
  3. AC = ^@\sqrt{ AB^2 + BC^2 }^@
    = ^@\sqrt{ 8^2 + 15^2 }^@
    = 17 cm
  4. The area of the triangle ACD can be calculated using Heron's formula.
    S =  
    CD + DA + AC
    2
     
    =  
    16 + 17 + 17
    2
     
    = 25 cm
  5. The area of the triangle ACD = √ S(S - CD)(S - DA)(S - AC)

    = √ 25(25 - 16)(25 - 17)(25 - 17)
    = 120 cm2
  6. The area of the quadrilateral ABCD = Area(ABC) + Area(ACD) = 60 + 120 = 180 cm2.

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