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9. Two roads run from a definite place with an angle of 135 o in two dinrections.
   Two persons move from the definite place in two directions with the speed of 7
   km per hour and 5 km per hour respectiv ely. What will be the direct distance
   between them after 4 hours?


10. If the lengths of the perpendiculars from a point interior of an equilateral triangle
    to three sides are 6 cm., 7 cm., 8 cm. respectively; find the length of sides of the
    triangle and the area of the triangular region.
    16 ⋅2 Area of Quadrilateral Region
    (1) Area of rectangular region
    Let, the length of AB a, breadth
    BC b and diagonal AC d, of rectangleABCD.
    We know, the diagonal of a rectangle divides.
    the rectangle into two equal triangular regions.

? Area of the rectangle ABCD 2 uareaof 'ABC= u a˜b ab
2

1

2

perimeter of the rectangular region, s 2 (ab)
the'ABC is right angled.
AC^2 AB^2 BC^2 or, d^2 a^2 b^2 ; ?d a^2 b^2
(1) Area of square region
Let the length of each side of a square ABCD
bea and diagonal d. The diagonal AC
divides the square region into two equal
triangular regions.
? Area of square region ABCD = 2 u area of 'ABC

= u a˜a
2

1

2 = a^2

Observe that, the perimeter of the square region s 4 a

and diagonal d a^2 a^2 2 a^2 2 a
(3) Area of parallelogram region.
(a) Base and height are given.
Let, the base AB b
and height DE h of parallelogramABCD
The diagonal BD divides the parallelogram into
two equal triangular regions.
? The area of parallelogram ABCD = 2 u area of 'ABD

= u b˜h

2

1

2

=bh