Advertisements
Advertisements
Question
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.
Advertisements
Solution
For ΔABC,
AC2 = AB2 + BC2
(5)2 = (3)2 + (4)2
Therefore, ΔABC is a right-angled triangle, right-angled at point B.
Area of ΔABC`= 1/2xxABxxBC=1/2xx3xx4=6 cm^2`
For ΔADC,
Perimeter = 2s = AC + CD + DA = (5 + 4 + 5) cm = 14 cm
s = 14/2 = 7 cm
By Heron’s formula,
`"Area of triangle "=sqrt(s(s-a)(s-b)(s-c))`
`"Area of "triangle ADC=[sqrt(7(7-5)(7-5)(7-4))]cm^2`
`=(sqrt(7xx2xx2xx3))cm^2`
`=2sqrt21 cm^2`
= (2 x 4.583) cm2
= 9.166 cm2
Area of ABCD = Area of ΔABC + Area of ΔACD
= (6 + 9.166) cm2
= 15.166 cm2
= 15.2 cm2 (approximately)
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.
Find the area of a rhombus whose perimeter is 80 m and one of whose diagonal is 24 m.
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 4 cm.
Find the area of an equilateral triangle having each side x cm.
The base and hypotenuse of a right triangle are respectively 5 cm and 13 cm long. Its area is ______.
The lengths of the sides of Δ ABC are consecutive integers. It Δ ABC has the same perimeter as an equilateral triangle with a side of length 9 cm, what is the length of the shortest side of ΔABC?
Find the area of a quadrilateral ABCD whose sides are AB = 13 cm, BC = 12 cm, CD = 9 cm, AD = 14 cm and diagonal BD = 15 cm
A park is in the shape of a quadrilateral. The sides of the park are 15 m, 20 m, 26 m and 17 m and the angle between the first two sides is a right angle. Find the area of the park
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.
