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` [โต๐๐
=3 ๐๐
=4 ๐๐๐ ๐๐=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 rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?
A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.
Area of PQRS = Area of PQR + Area of ΔPQS = (6+9.166)๐๐2=15.166๐๐2
Two parallel side of a trapezium are 60 cm and 77 cm and other sides are 25 cm and 26 cm. Find the area of the trapezium.
If the area of an isosceles right triangle is 8 cm2, what is the perimeter of the triangle?
If every side of a triangle is doubled, then increase in the area of the triangle is
A square and an equilateral triangle have equal perimeters. If the diagonal of the square is \[12\sqrt{2}\] cm, then area of the triangle is
A land is in the shape of rhombus. The perimeter of the land is 160 m and one of the diagonal is 48 m. Find the area of the land.
The adjacent sides of a parallelogram measures 34 m, 20 m and the measure of the diagonal is 42 m. Find the area of parallelogram
