Re: The area of region ABCD
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30 Aug 2025, 08:22
The figure is a parallelogram $A B C D$. To find the area of the parallelogram, use the formula:
$$
\(\text { Area }=\text { base } \times \text { height }\)
$$
Here, $A D$ is the side with length 7 units, and the height corresponds to the perpendicular distance from point $B$ to line $A D$.
We are given:
- The angle at $B$ is $\(130^{\circ}\)$
- The side $A D=7$
- The perpendicular height can be found using $A B \sin ($ angle $)$, but since $A B$ is not explicitly given, we note that $A B=C D$.
Because the side $B C=7$ units (opposite to $A D$ ), let's take $B C$ as the side and calculate height from $B$.
Height $h$ is:
$$
\(h=B C \sin \left(130^{\circ}\right)=7 \sin \left(130^{\circ}\right)\)
$$
Calculate $\(\sin \left(130^{\circ}\right)\)$ :
$$
\(\sin \left(130^{\circ}\right)=\sin \left(180^{\circ}-130^{\circ}\right)=\sin \left(50^{\circ}\right) \approx 0.766\)
$$
So,
$$
\(h=7 \times 0.766=5.36\)
$$
The base length $A B$ is given as 5 units.
Area $=$ base $\(\times\)$ height $\(=5 \times 5.36=26.8\)$
Comparing quantities:
- Quantity A: 26.8
- Quantity B: 35
Since $\(26.8<35\)$, Quantity B is greater.
Answer: Quantity B is greater.