Question

List all the formulas in the chapter herons formula for grade 9.With examples of each.
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Answer 1

Answer:

To find the area of a quadrilateral, when one of its diagonal value and the sides are given, the area can be calculated by splitting the given quadrilateral into two triangles and use the Heron's formula. Example :A park, in the shape of a quadrilateral ABCD, has ∠C=90∘, AB = 9 cm, BC = 12 cm, CD = 5 cm and AD = 8 cm.

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Answer 2

Step-by-step explanation:

Area = ½ × base × Height

List of Formulas to Find Isosceles Triangle Area:

Using base and Height A = ½ × b × h

Using all three sides A = ½[√(a2 − b2 ⁄4) × b]

Using the length of 2 sides and an angle between them A = ½ × b × c × sin(α)

Using two angles and length between them A = [c2×sin(β)×sin(α)/ 2×sin(2π−α−β)]

Area formula for an isosceles right triangle A = ½ × a2

The Altitude of an Isosceles Triangle = √(a2 − b2/4)

Thus,

Area of Isosceles Triangle Using Only Sides = ½[√(a2 − b2 /4) × b]

b = base of the isosceles triangle

h = height of the isosceles triangle

a = length of the two equal sides

area of isosceles triangle = b/2 × √(a2 − b2/4)

Formula for Isosceles Right Triangle Area= ½ × a2

Perimeter of Isosceles Right Triangle Formula

P = a(2+√2)

Herons formula: Area = √[s(s−a)(s−b)(s−c)]