Mathematics
In adjoining figure, BD is a diagonal of quad. ABCD. Show that ABCD is a parallelogram and calculate the area of ∥ gm ABCD.
Answer
Given,
BD = 8 cm
AB = DC = 6 cm.
∠DBA = ∠BDC = 90°
Thus, BD is perpendicular to both AB and DC.
∴ AB ∥ DC
Since one pair of opposite sides are equal and parallel, thus ABCD is a parallelogram.
We know that,
Area of ∥gm = Base × Height
Area of ∥gm ABCD = AB × BD
= 6 × 8
= 48 cm2.
Hence, proved that ABCD is a parallelogram and area of ∥gm ABCD is 48 cm2.
Related Questions
In a ∥ gm ABCD, it is given that AB = 16 cm and the altitudes corresponding to sides AB and AD are 6 cm and 8 cm respectively. Find the length of AD.
Find area of rhombus, the lengths of whose diagonals are 18 cm and 24 cm respectively.
Find area of trapezium, whose parallel sides measure 10 cm and 8 cm respectively and the distance between these sides is 6 cm.
Show that the line segment joining the mid-points of a pair of opposite sides of a parallelogram, divides it into two equal parallelogram.
