Mr.Ashok has a plot of a quadrilateral shaped with vertices (0, 0), (a, 0), (a, b), and (0,b)
QUESTION 1: The type of quadrilateral shaped plot is
(a) square (b) rhombus (c) rectangle (d) trapezium
QUESTION 2: What will be the perimeter of a plot?
(a) (a+b) units (b) 2(a+b) units (c) ab units (d) 2ab units
QUESTION 3: What will be the area of a plot?
(a) 0 sq.units (b)a2 sq.units (c)b2 sq.units (d) ab sq.units
QUESTION 4: The area of each triangular part of a plot will be
(a) ab sq.units (b) 2ab sq.units (c)1/2 ab sq units (d) ¼ ab sq units
QUESTION 5: The ratio of areas of these two triangular parts of a plot will be
(a) 1:2 (b) 2:1 (c) 1:1 (d) 1:4
Answers
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Answer:
QUESTION 1: (c) Rectangle
QUESTION 2: (b) 2(a+b) units
QUESTION 3: (d) ab sq. units
QUESTION 4: (c) 1/2 ab sq. units
QUESTION 5: (c) 1:1
Step-by-step explanation:
QUESTION 1: (c) Rectangle
Since the value of 'a' and 'b' are unknown and all these points when joined, they will form a closed figure with 90° [See the attached figure]
QUESTION 2: (b) 2(a+b) units
The X-Axis of points A, and D are 0, meaning
The Length of the Rectangle = a; and
The Breadth of the Rectangle = b
So, the perimeter of the rectangle = 2(l+b) nothing but 2(a+b)
QUESTION 3: (d) ab sq. units
Area of rectangle
= (l×b) [Length and Breadth shown in Q2]
= a×b
= ab sq. units
QUESTION 4: (c) 1/2 ab sq. units
A diagonal in a rectangle separates it into 2 right-angled triangles
QUESTION 5: (c) 1:1
As the 2 triangles formes will be equal.
Given : Mr. Ashok has a plot of a quadrilateral shaped with vertices (0, 0), (a, 0), (a, b), and (0,b)
To Find :
The type of quadrilateral shaped plot
What will be the perimeter of a plot
What will be the area of a plot
The area of each triangular part of a plot will be
The ratio of areas of these two triangular parts of a plot will be
Solution:
Let say points are
A ( 0 , 0) , B ( a , 0) , C( a , b) , D , ( 0 , b)
Slope of AB = Slope of CD = 0 Hence Parallel to x axis
Slope of BC = Slope of AD = b/0 Hence parallel to y axis
Hence adjacent lines are perpendicular
AB length = CD length = a
BC length = AD length = b
Quadrilateral formed is Rectangle
Perimeter = 2(a + b) units
Area of the plot = ab sq units
Diagonal Divide rectangle in two equal parts.
The area of each triangular part of a plot will be = (1/2)ab sq units
The ratio of areas of these two triangular parts of a plot will be 1 :1
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