Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
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.
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.
A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm and 35 cm (see the given figure). Find the cost of polishing the tiles at the rate of 50p per cm2.
Area of PQRS = Area of PQR + Area of ΔPQS = (6+9.166)𝑐𝑚2=15.166𝑐𝑚2
A park, in the shape of a quadrilateral ABCD, has ∠C = 900, AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m How much area does it occupy?
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.
The perimeter of a triangullar field is 144 m and the ratio of the sides is 3 : 4 : 5. Find the area of the field.
The base and hypotenuse of a right triangle are respectively 5 cm and 13 cm long. Its area 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
The area of an isosceles triangle having base 2 cm and the length of one of the equal sides 4 cm, is ______.
