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Area of Triangles

Our Lesson. Area of Triangles. Warm Up. 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

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Area of Triangles

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  1. Our Lesson Area of Triangles

  2. Warm Up • 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 • Find the base of a parallelogram whose area is 75 m²and corresponding altitude is 15 m. Answer: 5 m 5. Find the base of a hall whose area is 1800m²and height is 300 m. Answer: 6 m Confidential

  3. Let’s review what we have learnt in the last lesson 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 Confidential

  4. Properties In a parallelogram, • The opposite sides are equal i.e. AB = DC and AD = BC • The opposite angles are equal i.e. Angle A = Angle C Angle D = Angle B • Any two adjacent angles are supplementary i.e. Angle A + Angle B = 180° Angle B + Angle C = 180° Confidential

  5. Let us start 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 = whereb  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. 1 2 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 . The area of a triangle is given by "half of base times height“. ½ x b x h ½ x 10cm x 4cm 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. The area of a triangle is given by "half of base times height“. ½ x b x h ½ x 7yd x 11yd 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. The area of a triangle is given by "half of base times height“. ½ x b x h ½ x b x 10in. 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. 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: • Base = 5 cm, height = 2 cm Answer= 5 cm2 • Base = 7 yd, height = 8 yd Answer= 28 yd2 • Base = 15 m, height = 2 m Answer= 15 m2 • Base = 6 ft, height = 6 ft Answer= 18 ft2 • Base = 3.6 in, height = 4 in Answer= 7.2 in2 Confidential

  12. Your Turn Find the base of the triangle: • area = 132 m2, height = 12 m Answer = 22 cm • area = 77 yd2, height = 11 yd Answer= 14 yd • area = 15 cm2, height = 2 cm Answer= 15 cm Find the height of the triangle: • Base = 6 ft, area = 6 ft2Answer= 2 ft • Base = 9 in, area = 36 in2Answer= 8 in Confidential

  13. Break Time Confidential

  14. Let us play a game Click here to play Confidential

  15. Q1: In the given figure • What is the base and height? • Find the area of the given triangle. Solution: • From the figure it is clear that Base = 6 cm Height = 7.5 cm Confidential

  16. Solution: • Base = 6 cm Height = 7.5 cm Area of Triangle = = = 22.5 cm2 The area of the given triangle is22.5 cm2 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 = wherebis 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 Be sure to keep practicing Confidential

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