Question

One diagonal of a parallelogram is 7cm and the perpendicular distance of this diagonal from either of the outlying vertices is 27cm. The area of the parallelogram (in sq.cm) is?
A. 180
B. 183
C. 189
D. 198

Answer 1

Hint- In Geometry, a parallelogram is a two-dimensional figure with four sides. It is a special case of the quadrilateral. Here we will calculate the area of one of the triangles using formula area = ½ bh, and then multiply it by 2 to get the total area of the parallelogram.

Complete step-by-step answer:
The area of a parallelogram is the region bounded by the parallelogram in a given two-dimension space.

Length of diagonal AC = 7cm and BM = DN =27cm
The diagonal of the parallelogram divides it into two congruent triangles. So, their area will be equal.
Area of parallelogram = 2 $ \times $area of ${\Delta ACD}$
                                        = 2 $ \times $$\dfrac{{{1}}}{{{2}}}{{ \times 27 \times 7}}$
                                         = 189 ${\text{c}}{{\text{m}}^{\text{2}}}$
So, the area of the given parallelogram is 189 ${\text{c}}{{\text{m}}^{\text{2}}}$.
Therefore, option (C) is the correct answer.

Note- To recall, a parallelogram is a special type of quadrilateral which has four sides and the pair of opposite sides are parallel. In a parallelogram, the opposite sides are of equal length and opposite angles are of equal measures. Since the rectangle and the parallelogram have similar properties, the area of the rectangle is equal to the area of a parallelogram.