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Answer: 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
