Question
Find the area of the quadrilateral ABCD in which BCD is an equilateral triangle, each of whose sides is 26cm, AD = 24cm and BAD = . Also, find the perimeter of the quadrilateral. (Given, = 1.73.)
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Text solution
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In ABD
Using the Pythagoras theorem
By substituting the values
On further calculation
By subtraction
By taking out the square root
So we get
Base = AB = 10cm
We know that area of
By substituting the values
Area of
On further calculation
Area of
We know that the area of
By substituting the values
Area of
So we get Area of
So we get area of quadrilateral ABCD = Area of ABD + Area of BCD
By substituting the values
Area of quadrilateral ABCD = 120 + 29237
By addition
Area of quadrilateral ABCD = 412.37 cm
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 and perimeter is
Using the Pythagoras theorem
By substituting the values
On further calculation
By subtraction
By taking out the square root
So we get
Base = AB = 10cm
We know that area of
By substituting the values
Area of
On further calculation
Area of
We know that the area of
By substituting the values
Area of
So we get Area of
So we get area of quadrilateral ABCD = Area of ABD + Area of BCD
By substituting the values
Area of quadrilateral ABCD = 120 + 29237
By addition
Area of quadrilateral ABCD = 412.37 cm
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 and perimeter is
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| Question Text | Find the area of the quadrilateral ABCD in which BCD is an equilateral triangle, each of whose sides is 26cm, AD = 24cm and BAD = . Also, find the perimeter of the quadrilateral. (Given, = 1.73.) |
| Answer Type | Text solution:1 |
| Upvotes | 150 |
