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.
Radha made a picture of an aeroplane with coloured papers as shown in the given figure. Find the total area of the paper used.
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.
Find the area of a quadrilateral ABCD in which AD = 24 cm, ∠BAD = 90° and BCD forms an equilateral triangle whose each side is equal to 26 cm. (Take √3 = 1.73)
Find the area of an equilateral triangle having each side x cm.
If each side of a equilateral triangle is tripled then what is the percentage increase in the area of the triangle?
The base and hypotenuse of a right triangle are respectively 5 cm and 13 cm long. Its area is ______.
If the area of an isosceles right triangle is 8 cm2, what is the perimeter of the triangle?
In the given figure, the ratio AD to DC is 3 to 2. If the area of Δ ABC is 40 cm2, what is the area of Δ BDC?
If the length of a median of an equilateral triangle is x cm, then its area is
