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Question

Find the sum of areas of triangle ABC and AEC as shown in the figure given below.

A
be+eh2 unit2
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B
bd+ah2 unit2
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C
b(d+c)+eh2 unit2
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D
bd+eh2 unit2
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Solution

The correct option is D bd+eh2 unit2


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

=db2 unit2

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

=eh2 unit2

Hence, the sum of two triangles is
Area of a triangle ABC + Area of a triangle AEC =bd2+eh2

=bd+eh2 unit2

Option (d) is correct.

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