find the area of a quadrilateral ABCD in which ab is equal to 3 cm BC equal to 4 cm CD is equal to 4 cm equal to 5 cm and ac is equal to 5 cm
Answers
Step-by-step explanation:
find the area of a quadrilateral ABCD in which ab is equal to 3 cm BC equal to 4 cm CD is equal to 4 cm equal to 5 cm and ac is equal to 5 cm
Answer:
For ΔABC
a = 4 cm
b = 5 cm
c = 3 cm
∵ a2 + c2 = b2
For ΔABCa = 4 cmb = 5 cmc = 3 cm∵ a2 + c2 = b2
∴ ΔABC is righ
∴ ΔABC is right angled with ∠B = 90°.
∴ Area of right triangle ABC
equals 1 half cross times space Base space cross times space Height
equals space 1 half cross times 3 cross times 4 equals 6 space cm squared
For ΔACD
a = 4 cm b = 5 cm
c = 5 cm
therefore space space space space space space space straight s space equals space fraction numerator straight a plus straight b plus straight c over denominator 2 end fraction
space space space space space space space space space space space equals space fraction numerator 4 plus 5 plus 5 over denominator 2 end fraction equals 14 over 2 equals 7 space cm
∴ Area of the ΔACD
equals space square root of straight s left parenthesis straight s minus straight a right parenthesis left parenthesis straight s minus straight b right parenthesis left parenthesis straight s minus straight c right parenthesis end root
equals space square root of 7 left parenthesis 7 minus 4 right parenthesis left parenthesis 7 minus 5 right parenthesis left parenthesis 7 minus 5 right parenthesis end root
equals space square root of 7 left parenthesis 3 right parenthesis left parenthesis 2 right parenthesis left parenthesis 2 right parenthesis end root equals 2 square root of 21 space cm squared
= 2 x 4.6 cm2 (approx.)
= 9.2 cm2 (approx.)
∴ Area of the quadrilateral ABCD
= Area of ΔABC + Area of ΔACD
= 6 cm2 + 9.2 cm2
= 15.2 cm2, (approx.)