[tex]\text{Area}=115m^2[/tex]
Explanation
Step 1
the area of a parallelogram is given by:
[tex]\text{Area}=\text{ base}\cdot heigth[/tex]
in this problem, we dont know the heigth, but we know an angle, and the adjacent side of the rigth triangle( the rigth side of the parallelogram), we can use this to find the heigth
then
Let
opposite side= heigth= h
adjancent side= 5
angle = 45
we need a function that relates, sides and angle,so
[tex]\tan \emptyset=\frac{opposite\text{ side}}{\text{adjacent side}}[/tex]
replace
[tex]\begin{gathered} \tan 45=\frac{h}{\text{5}} \\ \text{Multiply both sides by 5} \\ 5\text{ tan 45=}\frac{h}{5}\cdot5 \\ h=5\text{ tang 45} \\ h=5 \end{gathered}[/tex]
Step 2
now, we have
heigth=5 m
base = 23 m
replace in the formula
[tex]\begin{gathered} \text{Area}=\text{ base}\cdot heigth \\ \text{Area}=\text{ 23 m}\cdot\text{ 5 m} \\ \text{Area}=115m^2 \end{gathered}[/tex]
so, the answer is 115 sqaure meters
I hope this helps you
