Some Common Mistakes while Selecting the Base and the Height of any Triangle
Find the sum ...
Question
Find the sum of areas of triangle ABC and AEC as shown in the figure given below.
A
be+eh2unit2
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B
bd+ah2unit2
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C
b(d+c)+eh2unit2
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D
bd+eh2unit2
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Solution
The correct option is Dbd+eh2unit2
→ Area of a triangle ABC
The perpendicular line drawn from the vertex 'A' to the extended line BC is called height of the triangle ABC and it is equal to b.
Since, AD is perpendicular to extended line BC, BC is the base of triangle ABC.
Base of the triangle ABC =BC=d unit
Height of the triangle =AD=b unit
As we know, Area of△ABC=12×Base×Height
=12×d×b
=db2unit2
→ Area of a triangle AEC
The perpendicular line drawn from the vertex 'E' to the line AC is called height of the triangle ABC and it is equal to h.
Since, EF is perpendicular to line AC, AC is the base of triangle ABC.
Base of the triangle AEC =AC=e unit
Height of the triangle =EF=h unit
As we know, Area of△ABC=12×Base×Height
=12×e×h
=eh2unit2
Hence, the sum of two triangles is
Area of a triangle ABC + Area of a triangle AEC =bd2+eh2