4. Find the area of a quadrilateral ABCD whose sides
AB, BC, CD and DA are 9 m, 40 m, 28 m and 15 m
respectively and the angle between the first two
sides is a right angle.
of the quadrilateral
Answers
Step-by-step explanation:
The answer is given in the form of photo copy.
Answer:
Area of quadrilateral = 126 m²
Step-by-step explanation:
In ΔABC,
(Hypo.)² = (Per.)² + (Base)² (Pythagoras theorem)
⇒ AC² = BC² + AB²
⇒ AC² = 40² + 9²
⇒ AC² = 1600 + 81
⇒ AC = √1681
⇒ AC = 41 m
Area of ΔCAD - a = 15 m
b = 41 m
c = 28 m
s = (a + b + c) / 2
= (15 + 41 + 28) / 2
= (84) / 2
= 42 m
area = √[s(s-a)(s-b)(s-c)]
= √[42 * (42 - 15) * (42 - 41) * (42 - 28)]
= √[42* 27 * 1 * 14 ]
= √(15876)
area of ΔCAD = 126 m²
Area of ΔABC = 1/2 * Base * Height
= 1/2 * 9 * 40
= 180 m²
Area of quad. (ABCD) = area of ΔCAD + area of ΔABC
= 126 m² + 180 m²
= 306 m²
HOPE THIS HELPS YOU
