Question

What is the area of Figure ABCD?

Answer 1

66 in^2.

Explanation:

We can use the formula for the area of a trapezoid:

Area = (h/2) (a + b) where h = the height and a and b are the lengths of the opposite parallel lines.

so the Area of ABCD = (6/2)*(10 + 12)

= 3 * 22

= 66 in^2.

Answer 2

For this case we have that the area of the figure is given by the sum of the area of a rectangle plus the area of a triangle.

By definition, the area of a reactangle is given by:

`A = a * b`

Where:

a, b:they are the sides of the rectangle.

According to the figure we have:

`a = 10\\b = 6`

Substituting we have:

`A = 10 * 6\\A = 60`

Thus, the area of the rectangle is
`60in ^ 2`

On the other hand, the area of a triangle is given by:

`A = \frac {b * h} {2}`

Where:

b is the base and h is the height of the triangle.

According to the figure we have to:

`b = 12-10 = 2\\h = 6`

Substituting in the formula:

`A = \frac {2 * 6} {2} = \frac {12} {2} = 6`

Thus, the area of the rectangle is
`6in ^ 2`

Then, the total area of the figure is:

`A_ {T} = 60in ^ 2 +6in ^ 2 = 66 \ in ^ 2`

Answer:

`66 \ in ^ 2`