Question

Find the area of the triangle. Round the answer to the nearest tenth.

A.
7.8 square units
B.
8.9 square units
C.
19.3 square units
D.
38.5 square units

Answer 1

The area of this triangle is 19.25
So the closest answer is C. 19.3

Hope this helps :)

Answer 2

19.3 square units .

Explanation:

∠D=∠F=52°

Opposite sides of equal angles are equal .

So, DE=EF =6.3

Now sum of all angles of triangle is 180°

So, ∠D+∠F+∠E = 180°

52°+52°+∠E =180°

104°+∠E =180°

∠E =180°-104°

∠E =76°

Now to find the length of DF we will use law of cosines

`c^2=a^2+b^2+2(a)(b) Cos E`

`DF^2=DE^2+EF^2+2(DE)(EF) Cos E`

`DF^2=6.3^2+6.3^2+2(6.3)(6.3) Cos 76^(\circ)`

`DF^2=79.38+79.38 (0.2419)`

`DF^2=98.582`

`DF=√(98.582)`

`DF=9.9`

Now we are supposed to find the area of triangle

To calculate the area of given triangle we will use the heron's formula :

`Area = √(s(s-a)(s-b)(s-c))`

Where
`s = (a+b+c)/(2)`

a,b,c are the side lengths of triangle

Now substitute the values :

`s = (6.3+6.3+9.9)/(2)`

`s =11.25`

`Area = √(11.25(11.25-6.3)(11.25-6.3)(11.25-9.9))`

`Area = 19.2907`

Hence the area of the triangle is 19.2907 ≈19.3 square units .