Example 1 :
Find the area of the figure given below.
Solution :
By observing the figure, it is a triangle.
Then, AC = base and BD = height
There are 4 units for the base and 3 units for height.
Finding the area :
Area of a triangle = 1/2 × base × height
= 1/2 × 4 × 3
Area = 6 sq.units
Example 2 :
Find the area and perimeter of the figure given below.
Solution :
By observing the figure, it is a square.
Then, HG = GF = EF = EH = side
There are 5 units for the side.
Finding the area :
Area of a square = side^{2}
= 5^{2}
Area = 25 sq.units
Finding the Perimeter :
Perimeter of a square = 4a
= 4(5)
Perimeter = 20 units
Example 3 :
Solution :
By observing the figure, it is a circle.
Then, OA = radius
There are 2 units for radius.
Finding the area :
Area of a circle = πr^{2}
= π(2^{2})
= 4π
Area = 4π sq.units
Draw the figure in a coordinate plane and find its area and perimeter.
Example 4 :
Triangle defined by A(3, 4), B(7, 4), and C(5, 7)
Solution :
By plotting the given points on the graph, we get
Now, there is a triangle.
Then, AB = base and CD = height
There are 4 units for the base and 3 units for height.
Finding the area :
Area of a triangle = 1/2 × base × height
= 1/2 × 4 × 3
Area = 6 sq.units
Example 5 :
Triangle defined by R(-2, -3), S(6, -3), and T(5, 4)
Solution :
By plotting the given points on the graph, we get
Now, there is a triangle.
Then, RS = base and TQ = height
There are 8 units for the base and 7 units for height.
Finding the area :
Area of a triangle = 1/2 × base × height
= 1/2 × 8 × 7
Area = 28 sq.units
Example 6 :
Rectangle defined by L(-2, -4), M(-2, 1), N(7, 1) and P(7, -4)
Solution :
By plotting the given points on the graph, we get
Now, there is a rectangle.
Then, LP = length and NP = width
There are 9 units for the length and 5 units for width.
Finding the area :
Area of a rectangle = length × width
= 9 × 5
Area = 45 sq.units
Finding the perimeter :
Perimeter of a rectangle = 2(length + width)
= 2(9 + 5)
= 2(14)
Perimeter = 28 units
Example 7 :
Square defined by W(5, 0), X(0, 5), Y(-5, 0) and Z(0, -5)
Solution :
By plotting the given points on the graph, we get
Now, there is a square.
But, we couldn’t calculate XY = YZ (side)
So, we are using the diagonals.
Here, d = 10 units
Finding the area :
Area of square using diagonals = 1/2 × d^{2}
= 1/2 × 10^{2}
= 1/2 × 100
Area = 50 sq.units
Finding the perimeter :
Perimeter of a square using diagonals = 4 × √(d^{2}/2)
= 4 × √(10^{2}/2)
= 4 × √100/2
= 4 × √50
= 4 × 5√2
= 20√2
Perimeter = 20√2 units
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