Question

In parallelogram ABCD, base AD is 15 and side AB is 8. What are the height and area of paralelogram ABCD if mDAB is 20?

Answer 1

Step-by-step explanation:

✰ $\underline{ \underline{ \large{ \tt{G\: I \: V \: E \: N}}}} :$

• AD = 15 , AB = 8 , $\angle$ DAB

✰ $\underline{ \underline{ \large{ \tt{T \: O \: \: F\: I \: N \: D}}}} :$

• Height & Area of the given parallelogram

✰ $\underline{ \underline{ \large{ \tt{S \: O

\: L \: U \: T\: I\: O \: N}}}} :$

In right angled triangle ABE :

• Hypotenuse ( h ) = 8
• Perpendicular ( p ) = h [ height ]
• $\theta$ = 20°

Now , Using trigonometric ratio :

$\large{ \tt{Sin \theta \: = \: \frac{Perpendicular}{Hypotenuse} }}$

Plug the known values :

⟶ $\large{ \tt{ Sin(20) = \frac{h}{8} }}$

⟶ $\large{ \tt{0.34 = \frac{h}{8}}}$

⟶ $\large{ \tt{h = 0.34 \times 8}}$

⟶ $\large{ \tt{h = 2.72}}$

Now , We have :

• Base ( b ) = 15
• Height ( h ) = 2.72

Finding the area of a parallelogram whose base and height are 15 and 2.72 respectively :

❀ $\underline{ \underline{ \text{Area \: of \: parallelogram = \tt{b *\: h}}}}$

⟶ $\large{ \tt{A = 15 *2.72}}$

⟶ $\large{ \tt{A = 40.8 \: {units}^{2} }}$

Hence , Our final answer :

$\large{ \boxed{ \sf{Height \: ( \: h \: ) = 2.72 \: units}}}$

$\large{ \boxed{ \sf{Area \: of \: parallelogram \: ( \:A \: ) = \: 40.8 \: {units}^{2} }}}$

Hope I helped ! ♡

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