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Confidential 2
1. Find the area of a parallelogram whose one side is 5 m and the corresponding altitude is 3 m.
Answer: 15 m²2. Find the area of a parallelogram whose base is 14 cm and
the corresponding height is 6cm. Answer: 84 cm²3. Find the altitude of a parallelogram whose area is 280 m² and
base is 14 m. Answer: 20 cm4. Find the base of a parallelogram whose area is 75 m²and
corresponding altitude is 15 m. Answer: 5 m
Warm Up
5. Find the base of a hall whose area is 1800m²and height is 300 m. Answer: 6 m
Confidential 3
Parallelogram is a quadrilateral in which pairs of opposite sides are parallel.
The distance between the pairs of opposite sides of a parallelogram is called an altitude of the parallelogram.
Area of the parallelogram is equal to the product of one of its bases and the corresponding altitude. i.e A = b * h
Let’s review what we have Let’s review what we have learnt in the last lessonlearnt in the last lesson
Confidential 4
In a parallelogram,
1. The opposite sides are equal i.e. AB = DC and AD = BC
2. The opposite angles are equal i.e. Angle A = Angle C
Angle D = Angle B
3. Any two adjacent angles are supplementary
i.e. Angle A + Angle B = 180° Angle B + Angle C = 180°
Properties
Confidential 5
What is a triangle?
A triangle is a kind of polygon that has three sides.
Examples of triangles:
Confidential 6
Area of a Triangle
The area of a triangle is given by "half of base times height“.
Area =
where
b is the length of the baseh is the height of the triangle.
Note: The height is the length of a line
segment perpendicular to the base of the triangle.
12
x b x h
Confidential 7
Finding Area of Triangle
Example1: Find the area of the triangle whose base is 10 cm and height is 4 cm.
Solution: Base = 10 cm. Height = 4 cm. Area of Triangle = = = 20 cm2 (After simplifying)
The area of the triangle is 20 cm2 .
hb2
1 The area of a triangle is given by "half of base times height“.
½ x 10cm x 4cm
½ x b x h
Confidential 8
Examples
Example2: Find the area of the triangle whose base is 7 yd and height is 11 yd.
Solution: Base = 7 yd. Height = 11 yd. Area of Triangle = = = 38.5 square yards
(After simplifying)The area of the triangle is 38.5 square yards.
hb2
1 The area of a triangle is given by "half of base times height“.
½ x 7yd x 11yd
½ x b x h
Confidential 9
Examples
Example 3: Find the base of the triangle whose area is 40 in2 and height is 10 in.
Solution: Area = 40 in2 Height = 10 in. Area of Triangle = 40in2 =
After simplification, we will get 40 = 5b b = 8 (by dividing both the sides by 5) The base of the triangle is 8 in.
hb2
1 The area of a triangle is given by "half of base times height“.
½ x b x 10in.
½ x b x h
Confidential 10
Examples
Example 4: Find the height of the triangle whose area is 15 ft2 and base is 5 ft.
Solution: Area = 15 ft2 Height = 5 ft. Area of Triangle = 15ft2 = After simplification, we will get 15 = 2.5b b = 6 ft (by dividing both the sides by 2.5) The height of the triangle is 6 ft.
hb2
1 The area of a triangle is given by "half of base times height“.
½ x b x h
½ x b x 5 ft
Confidential 11
Your Turn
Find the area:
1. Base = 5 cm, height = 2 cm Answer= 5 cm2
2. Base = 7 yd, height = 8 yd Answer= 28 yd2
3. Base = 15 m, height = 2 m Answer= 15 m2
4. Base = 6 ft, height = 6 ft Answer= 18 ft2
5. Base = 3.6 in, height = 4 in Answer= 7.2 in2
Confidential 12
Your Turn
Find the base of the triangle:6. area = 132 m2, height = 12 m Answer = 22 cm
7. area = 77 yd2, height = 11 yd Answer= 14 yd
8. area = 15 cm2, height = 2 cm Answer= 15 cm
Find the height of the triangle:9. Base = 6 ft, area = 6 ft2 Answer= 2 ft
10.Base = 9 in, area = 36 in2 Answer= 8 in
Confidential 13
Confidential 14
Let us play a game
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Confidential 15
Q1: In the given figure 1) What is the base and height?2) Find the area of the given
triangle.
Solution:1) From the figure it is clear
that Base = 6 cm Height = 7.5 cm
Confidential 16
Solution:2) Base = 6 cm Height = 7.5 cmArea of Triangle = =
= 22.5 cm2
The area of the given triangle is 22.5 cm2
hb2
1
½ x b x h
½ x 6 x 7.5
Confidential 17
Q2. The distance from the northern edge of Nicaragua to the southern edge is about 70 miles. The perpendicular distance from the western edge to the line along the eastern edge is about 268 miles. Estimate the area of Nicaragua.
A = ½ x b x h
A = 49,580sq.mi.
Confidential 18
Q3. The shape of New Hampshire resembles a right triangle with a base of 93 miles and a height of 180 miles. Estimate the area of New Hampshire.
Area = 8,370mi2
Confidential 19
Let Us Review
A triangle is a kind of polygon that has three sides.
The area of a triangle is given by "half of base times height“.
Area =
whereb is the length of the base.h is the height of the triangle.
½ x b x h
Confidential 20
You had a Great Lesson Today
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