Mathematics: Given: ∆afd, m ∠f = 90° ad = 14, m ∠d = 30° find: area of ∆afd

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Given: ∆afd, m ∠f = 90° ad = 14, m ∠d = 30° find:

natiem1803

03.01.2022

Area of ∆ADF is 42.44 m² .

Step-by-step explanation:

Since we have given that

AD = 14 m

m∠F = 90°

m∠D = 30°

We need to find the area of ∆ADF,

As we know the formula for " Area of triangle ":

$Area=\frac{1}{2}\times b\times h$

For this we need to find the base and height of the given triangle.

We will use the "Trigonometric Ratio ":

$\sin 60\textdegree=\frac{FA}{AD}\\\\\frac{\sqrt{3}}{2}=\frac{FA}{14}\\\\\frac{14}{2}\times \sqrt{3}=FA\\\\7\sqrt{3}=FA\\\\12.12\ m=FA$

Similarly, we will find the base.

$\cos 60\textdegree=\frac{DF}{AD}\\\\\frac{1}{2}=\frac{DF}{14}\\\\DF=\frac{14}{2}=7$

Now, we will apply the formula for Area of triangle :

$Area=\frac{1}{2}\times FA\times DF\\\\Area=\frac{1}{2}\times 12.12\times 7\\\\Area=42.435\\\\Area=42.44\ m^2$

Hence, Area of ∆ADF is 42.44 m² .

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