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In the adjoining figure, M and N are mid points of XY and XZ respectively. If the area of AMNY is 10cm?, find the area of AXYZ.​

A) 10 square centimeters
B) 20 square centimeters
C) 30 square centimeters
D) 40 square centimeters

User Garbo
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1 Answer

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Final answer:

The area of triangle AXYZ is 20 cm² since AMNY is a parallelogram occupying half of the triangle's area.

Step-by-step explanation:

If M and N are the midpoints of XY and XZ respectively in a triangle XYZ, then AMNY is a parallelogram. Since M and N are midpoints, AM = MX, and AN = NZ, which implies that each pair of opposite sides of the parallelogram are equal. Thus, the parallelogram AMNY is half of the area of the entire triangle XYZ. Given that the area of parallelogram AMNY is 10 cm², the area of triangle XYZ would be twice that of the parallelogram, which is 20 cm². Therefore, the correct answer is Option B) 20 square centimeters.

User Adavo
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