Question:One side of a rectangular field is 15 m and one of its diagonals is 17 m. Find the area of the field.
Other side` = sqrt((17))^2 - ((15))^2`
`= sqrt(289 - 225)`
`= sqrt(64) = 8 m.`
:. Area` = (15 xx 8) sq.m = 120 sq.m.`Question:Find the area of a triangle whose sides measure 13 cm, 14 cm and 15 cm.
Let a = 13, b = 14 and C = 15. Then, s `= 1/2 (a + b + c) = 21` :. (s - a) = 8, (s - b) = 7 and (s - c) = 6 :. Area` = sqrt(s (s - a) (s - b) (s - c)` `= sqrt(21 xx 8 xx 7 xx 6)` `= 84 cm^2`
Question:Find the area of a square, one of whose diagonal is 3.8 m long.
Area of the square` = 1/2 xx (diagonal)^2` `= (1/2 xx 3.8 xx 3.8) m^2 = 7.22 m^2`
Question:Find the area of an equilateral triangle each of whose sides is 8 cm long.
Area of the triangle` = sqrt(sqrt(3)/4 xx 8 xx 8) cm^2`
`= 16sqrt(3) cm^2`Question:Find the area of a right angle triangle whose base is 12 cm and hypotenuse 13 cm.
Height of the triangle` = sqrt((13))^2 - (12)^2`
`= sqrt(25) = 5 cm.`
:. Its area` = 1/2 xx Base xx Height`
`= ( 1/2 xx 12 xx 5) cm^2`
`= 30 cm^2`