# The Adjacent Sides of a Parallelogram Abcd Measure 34 Cm and 20 Cm, and the Diagonal Ac Measures 42 Cm. Find the Area of the Parallelogram. - Mathematics

The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram.

#### Solution

Given that adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm.
Area of parallelogram = Area of ΔADC + area of ΔABC
[∵ Diagonal of a parallelogram divides into two congruent triangles]
= 2 ×[𝐴𝑟𝑒𝑎 𝑜𝑓 Δ𝐴𝐵𝐶]
Now for Area of ΔABC
Let 2s = AB + BC + CA [∵ Perimeter of ΔABC]

⇒S=1/2(AB+BC+CA)

=S=1/2(34+20+42)

=1/2=(96)=48cm

∴Area of ΔABC =sqrt(s(s-ab))

=sqrt(48(48-34)(48-20)(48-42))

=sqrt(48(14)(28)(6))=336 cm^2

∴𝐴𝑟𝑒𝑎 𝑜𝑓 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑜𝑔𝑟𝑎𝑚 𝐴𝐵𝐶𝐷=2[𝐴𝑟𝑒𝑎 𝑜𝑓 Δ𝐴𝐵𝐶]=2×336=672 cm^2

Concept: Area of a Triangle by Heron's Formula
Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 17 Heron’s Formula
Exercise 17.2 | Q 9 | Page 20

Share