Answer:
Area of parallelogram = 9600 m²
Step-by-step explanation:
• We can find the measure of angle x using the cos rule:
[tex]160^2 = 100^2 +100^2 -2(100)(100) \cdot cos (x)[/tex]
Make x the subject of the equation:
⇒ [tex]20000 \cdot cos(x) = 100^2 +100^2 - 160^2[/tex]
⇒ [tex]cos(x) = -0.28[/tex]
⇒ [tex]x = cos^{-1} (-0.28)[/tex]
⇒ [tex]x = 106.26 \textdegree[/tex]
• Now we can find the area of one the triangles formed using the formula:
[tex]Area =\frac{1}{2} ab \cdot sin \theta[/tex]
where a and b are two sides of a triangle, and θ is the angle between them (angle x).
Substituting the values:
Area of one triangle = [tex]\frac{1}{2}[/tex] × (100)(100) × sin(106.26°)
= 4800 m²
• Since the parallelogram is formed by two such triangles, we have to double the area of the triangle to find the parallelogram's area:
Area of parallelogram = 2 × 4800
= 9600 m²
