Area
Area of triangles given in the figure.
In isoceles triangle, perpendicular drawn from vertex to the non-equal side bisects the non-equal side into two halves.
In a right angle triangle,
(Hypotenuse)² = (Perpendicular)² + (Base)²
Area of a triangle = (1/2) × Base × Height
Let us name first triangle with sides 20, 32 and 20 as triangle A and second triangle with sides 20, 24 and 20 as triangle B.
Let us assume that a perpendicular of height 'h' is drawn from vertex to the non-equal side of triangle A.
So, it will divide base of triangle into two halves each measuring
32 units / 2 = 16 units
Applying Pythagoras Theorem, in the half triangle which is formed after drawing perpendicular.
(20)² = (16)² + h²
h² = 400 - 256
h² = 144
h² = (12)²
h = 12 units
Calculating the area of triangle A,
Area of triangle A = (1/2) × 32 × 12 sq. units
Area of triangle A = 192 sq. units
Let us assume that a perpendicular of height 'H' is drawn from vertex to the non-equal side of triangle B.
24 units / 2 = 12 units
(20)² = (12)² + H²
H² = 400 - 144
H² = 256
H² = (16)²
H = 16 units
Calculating the area of triangle B,
Area of triangle B = (1/2) × 24 × 16 sq. units
Area of triangle B = 192 sq. units
Comparing,
Area of given two triangles is same.
Note : We can use Heron's formula too for calculating the area of given triangles as all sides of the triangle is given.
Solution :-
Answer :-
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Answers & Comments
Topic :-
Area
To Compare :-
Area of triangles given in the figure.
Concept :-
In isoceles triangle, perpendicular drawn from vertex to the non-equal side bisects the non-equal side into two halves.
In a right angle triangle,
(Hypotenuse)² = (Perpendicular)² + (Base)²
Area of a triangle = (1/2) × Base × Height
Solution :-
Let us name first triangle with sides 20, 32 and 20 as triangle A and second triangle with sides 20, 24 and 20 as triangle B.
Let us assume that a perpendicular of height 'h' is drawn from vertex to the non-equal side of triangle A.
So, it will divide base of triangle into two halves each measuring
32 units / 2 = 16 units
Applying Pythagoras Theorem, in the half triangle which is formed after drawing perpendicular.
(20)² = (16)² + h²
h² = 400 - 256
h² = 144
h² = (12)²
h = 12 units
Calculating the area of triangle A,
Area of triangle A = (1/2) × 32 × 12 sq. units
Area of triangle A = 192 sq. units
Let us assume that a perpendicular of height 'H' is drawn from vertex to the non-equal side of triangle B.
So, it will divide base of triangle into two halves each measuring
24 units / 2 = 12 units
Applying Pythagoras Theorem, in the half triangle which is formed after drawing perpendicular.
(20)² = (12)² + H²
H² = 400 - 144
H² = 256
H² = (16)²
H = 16 units
Calculating the area of triangle B,
Area of triangle B = (1/2) × 24 × 16 sq. units
Area of triangle B = 192 sq. units
Comparing,
Area of triangle A = 192 sq. units
Area of triangle B = 192 sq. units
Answer :-
Area of given two triangles is same.
Note : We can use Heron's formula too for calculating the area of given triangles as all sides of the triangle is given.
Topic :-
Area
To Compare :-
Area of triangles given in the figure.
Concept :-
In isoceles triangle, perpendicular drawn from vertex to the non-equal side bisects the non-equal side into two halves.
In a right angle triangle,
(Hypotenuse)² = (Perpendicular)² + (Base)²
Area of a triangle = (1/2) × Base × Height
Solution :-
Let us name first triangle with sides 20, 32 and 20 as triangle A and second triangle with sides 20, 24 and 20 as triangle B.
Let us assume that a perpendicular of height 'h' is drawn from vertex to the non-equal side of triangle A.
So, it will divide base of triangle into two halves each measuring
32 units / 2 = 16 units
Applying Pythagoras Theorem, in the half triangle which is formed after drawing perpendicular.
(20)² = (16)² + h²
h² = 400 - 256
h² = 144
h² = (12)²
h = 12 units
Calculating the area of triangle A,
Area of triangle A = (1/2) × 32 × 12 sq. units
Area of triangle A = 192 sq. units
Let us assume that a perpendicular of height 'H' is drawn from vertex to the non-equal side of triangle B.
So, it will divide base of triangle into two halves each measuring
24 units / 2 = 12 units
Applying Pythagoras Theorem, in the half triangle which is formed after drawing perpendicular.
(20)² = (12)² + H²
H² = 400 - 144
H² = 256
H² = (16)²
H = 16 units
Calculating the area of triangle B,
Area of triangle B = (1/2) × 24 × 16 sq. units
Area of triangle B = 192 sq. units
Comparing,
Area of triangle A = 192 sq. units
Area of triangle B = 192 sq. units
Answer :-
Area of given two triangles is same.
Note : We can use Heron's formula too for calculating the area of given triangles as all sides of the triangle is given.