25. Find the area of the quadrilateral ABCD in which AD = 24 cm, angle BAD = 90° and triangle BCD is an equilateral triangle having each side equal to 26 cm. Also, find the perimeter of the quadrilateral. [Given, v3 = 1.73.]
Answers
answer
In Δ ABD
Using the Pythagoras theorem
BD
2
=AB
2
+AD
2
By substituting the values
26
2
=AB
2
+24
2
On further calculation
AB
2
=676−576
By subtraction
AB
2
=100
By taking out the square root
AB=
100
So we get
Base = AB = 10cm
We know that area of ΔABD=
2
1
×b×h
By substituting the values
Area of ΔABD=
2
1
×10×24
On further calculation
Area of ΔABD=120cm
2
We know that the area of ΔBCD=
3
/4a
2
By substituting the values
Area of ΔBCD=(1.73/4)(26)
2
So we get Area of ΔBCD=292.37cm
2
So we get area of quadrilateral ABCD = Area of Δ ABD + Area of Δ BCD
By substituting the values
Area of quadrilateral ABCD = 120 + 29237
By addition
Area of quadrilateral ABCD = 412.37 cm
2
The perimeter of quadrilateral ABCD = AB + BC + CD + DA
By substituting the values
Perimeter = 10 + 26 + 26 + 24
So we get
Perimeter = 86cm
Therefore, the area is 412.37 cm
2
and perimeter is