Advertisements
Advertisements
Question
Find the area of a quadrilateral ABCD is which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.
Advertisements
Solution
For ΔPQR
`PQ^2=QR^2+RP^2`
`(5^2)=(3)^2+(4)^2` [∵𝑃𝑅=3 𝑄𝑅=4 𝑎𝑛𝑑 𝑃𝑄=5]
So, ΔPQR is a right angled triangle. Right angle at point R.
Area of ΔABC =`1/2xxQRxxRP`
`=1/2xx3xx4`
`=6cm^2`
For ΔQPS
Perimeter = 2s = AC + CD + DA = (5 + 4 + 5)cm = 14 cm
S = 7 cm
By Heron’s formulae
Area of Δle`sqrt(s(s-a)(s-b)(s-c))cm^2`
Area of Δle PQS `=sqrt(7(7-5)(7-4)(7-3))cm^2`
`=2sqrt(21)cm^2`
`=(2xx4.583)cm^2`
`=9.166cm^2`
Area of PQRS = Area of PQR + Area of ΔPQS = `(6+9.166)cm^2=15.166 cm^2`
APPEARS IN
RELATED QUESTIONS
A triangle and a parallelogram have the same base and the same area. If the sides of triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
The sides of a quadrilateral, taken in order are 5, 12, 14 and 15 meters respectively, and the angle contained by the first two sides is a right angle. Find its are
Find the area of an equilateral triangle having each side 4 cm.
The sides of a triangle are 50 cm, 78 cm and 112 cm. The smallest altitude is
If the area of an isosceles right triangle is 8 cm2, what is the perimeter of the triangle?
The sides of a triangle are 56 cm, 60 cm and 52 cm long. Then the area of the triangle is ______.
The area of an equilateral triangle with side `2sqrt(3)` cm is ______.
The sides of a triangle are 35 cm, 54 cm and 61 cm, respectively. The length of its longest altitude ______.
The area of an isosceles triangle having base 2 cm and the length of one of the equal sides 4 cm, is ______.
The area of the equilateral triangle is `20sqrt(3)` cm2 whose each side is 8 cm.
