Question

1. what is the area of abcd?
2. what is the length of diagonal bd?

Explanation:

Step1: Identify full diagonal AC

Given segment AO = 3.8 cm, diagonals of a rhombus bisect each other, so $AC = 2 \times AO$
$AC = 2 \times 3.8 = 7.6$ cm

Step2: Find half diagonal BO

In right triangle BOC (rhombus diagonals are perpendicular, so $\angle BOC=90^\circ$), side BC=5 cm, $OC=\frac{AC}{2}=3.8$ cm. Use Pythagorean theorem: $BO = \sqrt{BC^2 - OC^2}$
$BO = \sqrt{5^2 - 3.8^2} = \sqrt{25 - 14.44} = \sqrt{10.56} \approx 3.25$ cm

Step3: Calculate full diagonal BD

$BD = 2 \times BO$
$BD = 2 \times 3.25 = 6.5$ cm

Step4: Compute area of rhombus

Area of rhombus = $\frac{1}{2} \times AC \times BD$
$\text{Area} = \frac{1}{2} \times 7.6 \times 6.5$

Answer:

1. The area of ABCD is $24.7$ cm²
2. The length of diagonal BD is $6.5$ cm