Find the area and perimeter of quadrilateral ABCD given below if ab is equal to 8 cm is equal to 10 centimetre BD is equal to 12 centimetre is equal to 13 cm and angle DBC is equal to 90 degree
Answers
Hi there,
The question given above has some missing data. So, I have written the complete question and have attached the figure below for reference and solved it accordingly. Thanks
Q. Find the area and perimeter of the quadrilateral ABCD given below in which AB = 8 cm, AD = 10 cm, BD =12 cm, DC = 13 cm and angle DBC = 90 degree.
Answer:
Area = 70 cm²
Perimeter = 36 cm
Explanation:
Step 1:
In ∆ BDC, applying the Pythagoras theorem, we get
DC² = BD² + BC²
⇒ BC = √[DC² − BD²]
⇒ BC =√[13² - 12²]
⇒ BC =√[169 – 144]
⇒ BC = √25 = 5 cm
Step 2:
Considering △DBC,
Base, BD = 12 cm
Height, BC = 5 cm
∴ Area of triangle △DBC= ½ * base * height = ½ * 12 * 5 = 30 cm² ….. (i)
Step 3:
Now, considering △ABD,
We will find the area of triangle ABD by using Heron’s formula.
So, here a = 10 cm, b = 12 cm and c = 8 cm
∴ Semi-perimeter, S = (a+b+c)/2 = (10+12+8)/2 = 15 cm
∴ Area of △ABD,
= √[S(S−a)(S−b)(S−c)]
=√[15(15−10)(15−12)(15−8)]
=√[15 * 5 * 3 * 7]
=√[1575]
= 39.68 cm²
≈ 40 cm²….. (ii)
Step 4 :
Thus,
The area of quadrilateral ABCD,
= area of △DBC + area of △ABD
= 30 + 40 …… [substituting from (i) & (ii)]
= 70 cm²
And,
The perimeter of quadrilateral ABCD,
= AB + BC + CD + AD
= 8 + 5 + 13 + 10
= 36 cm
Hope this is helpful!!!!
