Question

Explanation would be appreciated. i don’t understand

Answer 1

(B) 28√3

Explanation:

The area of quadrilateral ABED is equal to the area of triangle CDE subtracted from the area of triangle ABC.

Area of triangle CDE:

Triangle ABC is equilateral. All sides have length 12.

AB = BC = AC = 12

BE = 8

BE + EC = BC

8 + EC = 12

EC = 4

In an equilateral triangle, all angles measure 60°.

m<C = 60°

m<CDE = 30°

Triangle CDE is a 30-60-90 triangle.

DE = EC√3

DE = 4√3

area of triangle CDE = bh/2

area of triangle CDE = (EC)(DE)/2

area of triangle CDE = (4)(4√3)/2

area of triangle CDE = 8√3

Area of triangle ABC:

Side AC is a base of triangle ABC.

AC = 12

(1/2)AC = 6

The altitude of triangle ABC from side AC to vertex B measures

h = 6√3

area of triangle ABC = bh/2

area of triangle ABC = (AC)(h)/2

area of triangle ABC = (12)(6√3)/2

area of triangle ABC = 36√3

area of quadrilateral ABED = area of triangle ABC - area of triangle CDE

area of quadrilateral ABED = 36√3 - 8√3

area of quadrilateral ABED = 28√3

Answer 2

`28√(3)`

Explanation:

The area of the big triangle is 1/2 b h = 1/2*6*(12^2 = 6^2 + x^2)

that ends up being
`√(108) = 36√(3)`

the small triangle are needs to be subtracted....

`(\left(4\cdot \:sin\left(90\right)\right))/(sin\left(30\right))` that is the length of the unknown side...

1/2 B * h of that triangle get you to
`8√(3)`

just subtract the two areas