Q3 of 16 Page 160

Compute the area of the quadrilateral shown below:

More elaborated diagram is as shown below:


Area of quadrilateral = area(ABC) + area(ACD) …..(1)


Triangle ABC is a right triangle.


Therefore, area(ABC) =


=


=


=


Also, using Pythagoras theorem, we have:





Now we find that all sides of triangle ACD are equal.


i.e. AC = CD = AD = 20 cm


Therefore, triangle ACD is an equilateral triangle.


Area of equilateral triangle ACD =


=


= 173.2 sq. cm


Therefore, from (1), we get:


Area of quadrilateral = area(ABC) + area(ACD)


= 96 sq. cm+ 173.2 sq. cm


= 269.2 sq. cm


Hence, area of the quadrilateral is 269.2 square centimetres.


More from this chapter

All 16 →
1

What is the area of the quadrilateral shown below?

 2

Prove that for any quadrilateral with diagonals perpendicular, the area is half the product of the diagonals.

 4

Compute the area of the parallelogram shown below:

 4

The three blue lines in the picture below are parallel:


Prove that the areas of the quadrilaterals ABCD and PQRS are in the ratio of the lengths of the diagonals AC and PR.


(i) How should the diagonals be related for the quadrilaterals to have equal area?


(ii) Draw two quadrilaterals, neither parallelograms nor trapeziums, of area 15 square centimetres.