Question

Can you please help with problem 23

Answer 1

$\\ \rm\longmapsto sin45=\dfrac{h}{22}$

$\\ \rm\longmapsto h=22sin45=22(0.71)=15.6in$

• Parallel sides of a parallelogram are equal.

$\\ \rm\longmapsto Area$

$\\ \rm\longmapsto Base(Height)$

$\\ \rm\longmapsto 26(15.6)=405.6in^2$

Answer 2

#22

• Find the height using the trigonometric ratio.
• Trigonometric ratio used here is:

$\boxed{\mathfrak{\sin( \theta)=\frac{perpendicular}{hypotenuse}}}$

• θ = 45°
• Perpendicular = ?
• Hypotenuse = 22

$\tt \: \sin(45 \degree) = \frac{p}{22}$

$\tt \: \frac{ \sqrt{2} }{2} = \frac{p}{22}$

$\tt \: 22 \sqrt{2} = 2p$

$\tt11 \sqrt{2} = p \: or \: p = 11 \sqrt{2}$

➪Therefore th value of perpendicular is 15.5 when rounded off...

#23

• Now, We will find the area with the help of height that we just found using the trigonometric ratio.
• The formula to find area of parallelogram is:

$\boxed{ \mathfrak{area = base \times height}}$

• Base = 26 in. [Since opposite sides of parallelogram are equal and parallel]
• Height = 15.5 in.

$\sf \: area = 26 \times 15.5 \\ \sf \: area = 403 \: {in}^{2}$

➪Thus, The area of parallelogram is 403 inch²...~