The three medians AX, BY and CZ of \\Delta\ABC intersect at point L. If the area of \\Delta\ABC is 30 {\cm}^{2}, then the area of the quadrilateral BXLZ is

SSC CHSL 19 Mar 2020 Shift 2 Paper

Question : 54 of 100

Marks: +1, -0

The three medians AX, BY and CZ of

\Δ\ABC

intersect at point L. If the area of

\Δ\ABC

30 {\cm}^{2}

, then the area of the quadrilateral BXLZ is

Solution:

Given,

Area of

\Δ\ABC=30 {\cm}^{2}

Since, AX, BY and CZ are the medians,
∴ Area of

\Δ\BLX={1}/{6} \×

Area of

\Δ\ABC

={1}/{6} \×30=5 {\cm}^{2}

Similarly, Area of

\Δ\BLZ=5 {\cm}^{2}

∴ Area of quadrilateral

=

Area of

(\Δ\BLX+\Δ\BLZ)

=5+5=10 {\cm}^{2}

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