What is the area of this figure?

  44 units²

Step-by-step explanation:

Dividing the figure as per the blue line, you have two triangles and a trapezoid. The triangles both have the same base (4) and height (3). The area of each of them is ...

  A = (1/2)bh = 1/2·4·3 = 6 . . . . units²

The area of the trapezoid with bases 5 and 3 and height 8 is given by ...

  A = (1/2)(b1 +b2)h = (1/2)·(5 + 3)·8 = 32 . . . . units²

Then the total area of the figure is the sum of the areas of the two triangles and the trapezoid:

  figure area = 2 × 6 units² + 32 units² = 44 units²

_____

Alternate solution

The area of a triangle is equal to that of a rectangle with the same base and half the height. Then the areas of the two triangles are equivalent to the area of the rectangle with the blue base and the top edge that is the green line.

Likewise, the area of a trapezoid is the product of its height and the length of its midline. That is the same as the area of the rectangle with the blue line as its top edge and the green line as its bottom edge.

In other words, the area of the figure is the same as the area of the green rectangle, which is 8 units × 5.5 units = 44 units².

A

Step-by-step explanation:

an=a1+(n-1)d

A(10)=15+(n-1)-2