In the figure shown- area of - AXS is equal to half the area of the parallelogram PQRSA- TrueB- False

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Triangles on the Same Base (Or Equal Bases) and Equal Areas Will Lie between the Same Parallels

In the figure...

Question

In the figure shown, area of ΔAXS is equal to half the area of the parallelogram PQRS

True

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False

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Solution

The correct option is A
True

ABRS and PQRS are parallelograms on the same base and between the same parallels. So, they are equal in area.

Triangle AXS and parallelogram ABRS are on the same base and between the same parallels.

So, Area of ΔAXS = $\frac{1}{2}$ (Area of ABRS) = $\frac{1}{2}$ (Area of PQRS)

Hence True.

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In the figure shown, area of ΔAXS is equal to half the area of the parallelogram PQRS

The correct option is A True ABRS and PQRS are parallelograms on the same base and between the same parallels. So, they are equal in area. Triangle AXS and parallelogram ABRS are on the same base and between the same parallels. So, Area of ΔAXS = 12 (Area of ABRS) = 12 (Area of PQRS) Hence True.