Question

Each side of rhombus is 13cm and the length of one diagonal is 24cm. Find the area of the rhombus

Answer 1

so first we should divide the diagonal
$24 \div 2 = 12$
now a triangle ABC
the angle is 90degree
now by Pythagoras theorem
(AC)²=(AB)²+(CA)²
now we have AC as 13cm
n AC=12
so it is
(13)²=(12)²+(CA)²
169=144+(CA)²
(CA)²=169-144
(CA)²=25
CA=5
so another diagonal =CA×2
=5×2
=10
so Area =½×10×24
=120cm²

Answer 2

$s = 13cm \\ d1 = 24cm \\ d2 = 2 \sqrt{ {13}^{2} - {12}^{2} } \\ =2 \sqrt{169 - 144 } \\ =2 \sqrt{25} \\ = 2 \times 5 \\ = 10 \\ area \: of \: rhombus = \frac{1}{2} d1 \times d2 \\ = \frac{1}{2} \times 24 \times 10 \\ = 12 \times 10 \\ = 120 {cm}^{2}$