Question

Find the area of the trapezoid. The figure is divided by the dashed line into a rectangle and a right triangle. Leave your answer in simplest radical form. IMPORTANT!

Answer 1

56 ft²

Explanation:

sin60 = a/8 ⇒ a = 8×sin(60)

=6,928203230276 ≈ 7

cos(60) = b/8 ⇒ b = 8×cos(60) = 4

area of the rectangle = 7×(10 - 4) = 7 × 6 = 42

area of the triangle = (4×7)/2 = 28/2 = 14

finally,

the area of the trapezoid = 42 + 14 = 56 ft²

Answer 2

The final answer is 32
`√(3)`.

Explanation:

The right triangle is a 30-60-90 triangle. Since we know that the hypotenuse of the triangle is 8, we can use the ratios to establish that the short leg is 4 and the long leg is 4
`√(3)`.

The length of the rectangle is 10ft minus the base of the triangle or 10-4 = 6ft. We can then say that the area of the rectangle is 24
`√(3)` ft.

Next, since we know the base and height of the triangle we can use the formula 1/2 b*h to determine that the triangle is 8
`√(3)`.

Finally, we add the areas together to a final answer of 32
`√(3)`