Question
Download Solution PDFThe area of ΔABC is 44 cm2. If D is the midpoint of BC and E is the midpoint of AB, then the area (in cm2) of ΔBDE is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Area of ΔABC = 44 cm2
BD = CD
AE = BE
Concept used:
The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and equal to half of it.
If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are similar.
The ratio of areas of two similar triangles is proportional to the squares of the corresponding sides of both triangles.
Calculation:
According to the concept,
DE ∥ AC, and AC = 1/2 × DE
Let BC = 2 unit, and BD = 1 unit
Area of ΔBDE/Area of ΔBCA = (BD/BC)2
⇒ Area of ΔBDE/44 = (1/2)2
⇒ Area of ΔBDE = (1/4) × 44 = 11 cm2
∴ The area of ΔBDE is 11 cm2
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