"Question 2 Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.
Class 9 - Math - Heron's Formula Page 206"
Answers
2s=(a+b+c)
s=(a+b+c)/2
Here ,s is called semi perimeter of a triangle.
The formula given by Heron about the area of a triangle is known as Heron's formula. According to this formula area of a triangle= √s (s-a) (s-b) (s-c)
Where a, b and c are three sides of a triangle and s is a semi perimeter.
This formula can be used for any triangle to calculate its area and it is very useful when it is not possible to find the height of the triangle easily . Heron's formula is generally used for calculating area of scalene triangle.
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Given, quadrilateral ABCD with AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm & diagonal AC = 5 cm.
Find the area of ∆ ABC and ∆ADC with the help of Herons formula.
In ΔABC,
By applying Pythagoras Theorem
AC²= AB²+BC²
5²=3² +4²
25 = 25
Thus, ΔABC is a right angled at B.
Area of ΔBCD = ½ × base × height.
Area of ΔBCD = 1/2 × 3 × 4 = 6 cm²
Now,
Semi perimeter of Δ (s)= (a+b+c)/2
Semi perimeter of ΔACD(s) = (5 + 5 + 4)/2
=14/2 cm = 7 cm
Using heron’s formula,
Area of ΔABD = √s (s-a) (s-b) (s-c)
= √7(7 – 5) (7 – 5) (7 – 4)
= √7 × 2 × 2 × 3
= 2√21cm². (√21=4.6)
= 2× 4.6
= 9.2 cm2 (approx)
Area of quadrilateral ABCD = Area of ΔABC + Area of ΔABD
= 6+ 9.2 = 15.2 cm²
Hence,the Area of quadrilateral ABCD =15.2cm²
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Hope this will help you....
Answer:not answerable
Step-by-step explanation: