Confidential2 1.Find the area of a parallelogram whose one side is 5 m and the corresponding altitude is 3 m. Answer: 15 m² 2. Find the area of a parallelogram whose base is 14 cm and the corresponding height is 6cm. Answer: 84 cm² 3. Find the altitude of a parallelogram whose area is 280 m² and base is 14 m. Answer: 20 cm 4.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

Confidential3 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 learnt in the last lesson

Confidential4 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

Confidential5 What is a triangle?  A triangle is a kind of polygon that has three sides.  Examples of triangles:

Confidential6 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 base h is the height of the triangle. Note: The height is the length of a line segment perpendicular to the base of the triangle x b x h

Confidential7 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 cm 2 (After simplifying) The area of the triangle is 20 cm 2. The area of a triangle is given by "half of base times height“. ½ x 10cm x 4cm ½ x b x h

Confidential8 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. The area of a triangle is given by "half of base times height“. ½ x 7yd x 11yd ½ x b x h

Confidential9 Examples Example 3: Find the base of the triangle whose area is 40 in 2 and height is 10 in. Solution: Area = 40 in 2 Height = 10 in. Area of Triangle = 40in 2 = After simplification, we will get 40 = 5b b = 8 (by dividing both the sides by 5) The base of the triangle is 8 in. The area of a triangle is given by "half of base times height“. ½ x b x 10in. ½ x b x h

Confidential10 Examples Example 4: Find the height of the triangle whose area is 15 ft 2 and base is 5 ft. Solution: Area = 15 ft 2 Height = 5 ft. Area of Triangle = 15ft 2 = 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. The area of a triangle is given by "half of base times height“. ½ x b x h ½ x b x 5 ft

Confidential11 Your Turn Find the area: 1.Base = 5 cm, height = 2 cm Answer= 5 cm 2 2.Base = 7 yd, height = 8 yd Answer= 28 yd 2 3.Base = 15 m, height = 2 m Answer= 15 m 2 4.Base = 6 ft, height = 6 ft Answer= 18 ft 2 5.Base = 3.6 in, height = 4 in Answer= 7.2 in 2

Confidential12 Your Turn Find the base of the triangle: 6.area = 132 m 2, height = 12 m Answer = 22 cm 7.area = 77 yd 2, height = 11 yd Answer= 14 yd 8.area = 15 cm 2, height = 2 cm Answer= 15 cm Find the height of the triangle: 9.Base = 6 ft, area = 6 ft 2 Answer= 2 ft 10.Base = 9 in, area = 36 in 2 Answer= 8 in

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Confidential14 Let us play a game Click here to play

Confidential15 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

Confidential16 Solution: 2)Base = 6 cm Height = 7.5 cm Area of Triangle = = = 22.5 cm 2 The area of the given triangle is 22.5 cm 2 ½ x b x h ½ x 6 x 7.5

Confidential17 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.

Confidential18 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 = 8,370mi 2

Confidential19 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 = where b is the length of the base. h is the height of the triangle. ½ x b x h

Confidential20 You had a Great Lesson Today Be sure to keep practicing