find out area of the following parallelogram
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Given
- The given figure is a triangle and it's sides measures :-
- AB = AC = 4 cm
- AD = 2 cm
To find
- Area of the triangle
Solution
Firstly, we will find the third side of the triangle by using pythagoras theorem.
In △ADC
By using pythagoras theorem,
H² = P² + B²
where,
- H = Hypotenuse of the triangle (Longest side).
- P = Perpendicular of the triangle.
- B = Base of the triangle.
____________________________
Hypotenuse = AC = 4 cm
Perpendicular = AD = 2 cm
Base = DC = ?
⟼ (4)² = (2)² + (DC)²
⟼ 16 = 4 + DC²
⟼ 16 - 4 = DC²
⟼ 12 = DC²
⟼ √12 = DC
⟼ ± √12 Reject - ve = DC
⟼ DC = √12 cm
Using formula to find the area of Isosceles triangle,
• Area of Isosceles triangle = ½ × b × h
where,
- b = base of the triangle
- h = height of the triangle
Base = 2 × DC = 2 × √12 = 4√3 cm
Height = AD = 2 cm
Substituting the given values,
⟼ Area = ½ × 4√3 × 2
⟼ Area = 4√3
⟼ Area = 4√3
The value of √3 = 1.732
⟼ Area = 4 × 1.732
⟼ Area = 6.928 cm²
Area of the given triangle = 6.928 cm²
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