These notes for CBSE Class 9 Mathematics, Chapter 12, focus on Heron's Formula. They explain how to calculate the area of a triangle using its side lengths. The semi-perimeter (s) of a triangle with sides a, b, and c is defined as s = (a+b+c)/2. Heron's formula states that the area of such a triangle is ?s(s-a)(s-b)(s-c). The notes also provide formulas for the area of an equilateral triangle with side 'a' as (?3/4)a² and the area of a triangle with base 'b' and altitude 'h' as (1/2)bh. Additionally, formulas for the area of a trapezium and specific triangle types are included. The chapter includes various solved examples and practice problems covering different scenarios, such as finding the area of a garden, the cost of leveling ground, and calculating areas of quadrilaterals and rhombuses. These notes are designed to help students revise the concepts and formulas for their exams.
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Section - A
Section - B
Q.6 Find the area of a triangular garden whose sides are 40m., 90m and 70m.
Q.7 Find the cost of leveling a ground in the form of a triangle with sides 16m, 12m and 20m at Rs. 4 per sq. meter.
Q.8 Find the area of a triangle, two sides of which are 8cm and 11cm and the perimeter is 32 cm.
Q.9 The area of an isosceles triangle is 12cm2. If one of its equal side is 5cm. Find its base.
Q.10 Find the area of a right triangle whose sides containing the right angle are 5cm and 6cm.
Q.11 Find the area of the adjoin figure
Section - C
Q.12 The diagonals of a rhombus are 24cm and 10cm. Find its area and perimeter.
Q.13 Two side of a parallelogram are 10cm and 7cm. One of its diagonals is 13cm. Find the area.
Q.14 A rhombus shaped sheet with perimeter 40 cm and one diagonal 12cm, is painted on both sides at the rate of ` 5 per m2. Find the cost of painting.
Q.15 The sides of a quadrilateral ABCD are 6cm, 8cm, 12cm and 14cm (taken in order) respectively, and the angle between the first two sides is a right angle. Find its area.
Q.16 The perimeter of an isosceles triangle is 32cm. The ratio if the equal side to its base is 3 : 2. Find the area of the triangle
Q.17 The sides of a triangular field are 41m, 40m and 9m. Find the number of flower beds that can be prepared in the field, if each flower bed needs 900cm2 space.
Q.18 The perimeter of a triangular ground is 420m and its sides are in the ratio 6 : 7 : 8. Find the area of the triangular ground.
Section - D
Q.19 Calculate the area of the shaded region
Q.20 If each sides of a triangle is double, then find the ratio of area of the new triangle thus formed and the given triangle.
Q.21 A field is in the shape of a trapezium whose parallel sides are 25m and 10m. If its non-parallel sides are 14m and 13m, find its area
Q.22 An umbrella is made by stitching 10 triangular pieces of cloth of 5 different colour each piece measuring 20cm, 50cm and 50cm. How much cloth of each colour is required for one umbrella?
Q.23 A triangle and a parallelogram have the same base and some area. If the sides of the triangle are 26cm, 28cm and 30cm and the parallelogram stands on the base 28cm, find the height of the parallelogram.
Heron's Formula is used to find the area of a triangle when the lengths of all three sides are known. The area is calculated as ?s(s-a)(s-b)(s-c), where a, b, and c are the side lengths and s is the semi-perimeter.
The semi-perimeter (s) of a triangle with sides a, b, and c is half of its perimeter, calculated as s = (a+b+c)/2.
The area of an equilateral triangle with side length 'a' is given by the formula (?3/4)a².
The area of a triangle is half the product of its base and corresponding altitude, i.e., Area = (1/2) × base × altitude.
The area of a trapezium is calculated as (1/2) × (sum of parallel sides) × (distance between parallel sides).
Yes, Heron's formula can be used to find the area of any triangle, regardless of its type (scalene, isosceles, equilateral), provided all three side lengths are known.
These notes provide a clear explanation of Heron's Formula and related concepts, along with practice problems, to help Class 9 students revise and prepare for their Mathematics exams.
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