Find the areas of the figures below. Show all work on for each problem.

 A = ≈28.55 cm²

Step-by-step explanation:

It is drawn as if it should be a triangle minus a rectangle with an area of

½(10)(13) - (7)(6) = 23 cm²

However it is not to scale.

The angle on the right side is

θ = arctan10/13 = 37.56859...°

Meaning the right triangle has a height of

h = 4tan37.56859 = 3.07692 cm

So the right triangle has an area of

Ar = ½(3.07692)(4) = 6.15384... cm²

The left hand side consists of a triangle over a rectangle

The height of the triangle is 4, the base is is 4/tan37.56859 = 5.2 cm

so the left area is

(2)(6) + ½(5.2)(4) = 22.4 cm²

So the sum of the areas of the two enclosed shapes is

A = 22.4 + 6.15384... = 28.55384... ≈28.55 cm²