10th Class Mathematics Coordinate Geometry Question Bank Case Based (MCQs) - Coordinate Geometry

The area of trapezium DEGF is:

A) 8 sq. units

B) 10 sq. units

C) 12 sq. units

D) 16 sq. units

Correct Answer: A

Solution :

The coordinates of the vertices D, E, G and F are \[(3,3),\]\[(6,3),\]\[(7,1)\]and \[(2,1)\].

(7,1) and (2,1). Now,

\[DE=\sqrt{{{(6-3)}^{2}}+{{(3-3)}^{2}}}=\sqrt{9+0}=3\] units

\[FG=\sqrt{{{(7-2)}^{2}}+{{(1-1)}^{2}}}=\sqrt{25+0}=5\] units

and height of trapezium = 2 units [from figure]

\[\therefore \] Area of trapezium

\[DEGF=\frac{1}{2}\times (DE+FG)\times height\]

\[=\frac{1}{2}\times (3+5)\times 2=8sq.\]unit

So, option [a] is correct.