The area of the figure formed by joining the mid-points of the adjacent sides of a rhombus with diagonals 12 cm and 16 cm is
a. 48 cm²
b. 64 cm²
c. 96 cm²
d. 192 cm²
Solution:
Let us join the midpoints AB, BC, CD, DA of rhombus ABCD and name it as M, N, O and P which forms MNOP
Join the line PN, PN || AB and PN || DC
If a triangle and a parallelogram are between the same parallels and on the same base, the area of triangle will be one half area of the parallelogram
From the question, parallelogram ABNP and triangle MNOP are on the same base PN and between same parallels PN and AB
Area of Δ MNP = 1/2 area of ABPN …. (1)
Area of Δ PON = 1/2 area of PNCD ….. (2)
So area of ABCD = 1/2 × d2 × d2
Using equations (1) and (2)
Area (MNOP) = Area of Δ MNP + Area of Δ PON
Substituting it we get
= 1/2 area of ABPN + 1/2 area of PNCD
= 1/2 (1/2 area of ABCD)
So we get
= 1/2 [1/2 × 12 × 16]
= 48 cm²
Therefore, the area of the figure is 48 cm².
✦ Try This: The area of the figure formed by joining the mid-points of the adjacent sides of a rhombus with diagonals 15 cm and 18 cm is
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 9
NCERT Exemplar Class 9 Maths Exercise 9.1 Sample Problem 1
The area of the figure formed by joining the mid-points of the adjacent sides of a rhombus with diagonals 12 cm and 16 cm is a. 48 cm², b. 64 cm², c. 96 cm², d. 192 cm²
Summary:
The area of the figure formed by joining the mid-points of the adjacent sides of a rhombus with diagonals 12 cm and 16 cm is 48 cm²
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