Sometimes, when you connect points, they make a figure, like a square, rectangle, triangle, etc.!
If the question requires to find area or perimeter of the shape created by connecting all the points, we have to use the formulae given below.
Rectangle :
Area = length x width
Perimeter = 2(length + width)
Square :
Area = Side x side
Perimeter = 4 (side)
Triangle :
Area = (1/2) x base x height
Perimeter = Sum of lengths of all sides
Problem 1 :
a) Plot the following points on the grid below :
A(3, 2), B(-3, 2),C(-3, -2), and D(3, -2).
b) Now, connect them.
c) What kind of shape do they make ?
d) Can you find the area of this figure ?
Solution :
a) Given points A(3, 2), B(-3, 2),C(-3, -2), and D(3, -2).
b)
c) The shape is rectangle.
d) area of the rectangle = l × w
= 6 × 4
= 24 unit^{2}
Problem 2 :
a) Plot the following points on the grid below : A(4, 1), B(1, 5), and C(-2, 1).
b) Now, connect them.
c) What type of polygon do they make ?
d) Find the area of this figure ?
Solution :
a) Given points A(4, 1), B(1, 5), and C(-2, 1).
b)
c) The type of polygon is triangle.
d) area of the triangle = 1/2 (b × h)
= 1/2 (6 × 4)
= 1/2 (24)
= 12 unit^{2}
Problem 3 :
Graph the points A(1, 1), B(5, 1), C(5, 4). What must be the coordinates of of point D if ABCD is a rectangle ?
D( , )
Solution :
Given points A(1, 1), B(5, 1), C(5, 4)
So, the missing point is (1, 4).
Problem 4 :
Graph the points P(-2, -4) and Q(2, -4). What are the coordinates of R and S if PQRS is a square ? (Two answers are possible).
R(__, __)
S(__, __)
Solution :
Given points P(-2, -4) and Q(2, -4).
So, the missing point is (2, 0) and (-2,0).
Problem 5 :
a) Graph and connect the given points : A(1, 7), B(1, 2),and C(5, 2).
b) Identify the figure (shape) :
c) Find the area of the figure :
Solution :
a)
b) The figure shape is right triangle.
c) The area of the right triangle = (1/2) x base x height
= (1/2) x 4 x 5
= 20/2
= 10 unit^{2}
Problem 6 :
a)Graph and connect the given points :
P(-1, 3), Q(5, 3), R(5, -2), and S(-1, -2).
b) Identify the figure (shape) :
c) Find the area of the figure :
Solution :
a)
b) The figure shape is rectangle.
c) area of the rectangle = l × w
= 6 × 5
= 30 unit^{2}
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM