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find the area of this figure. dimensions are in meters.

  2√46 + 25π/4 ≈ 33.2 . . . . m²

Step-by-step explanation:

The altitude of the triangle is given by the Pythagorean theorem. The right triangle of interest is the one that has 5√2 as its hypotenuse, and a leg of half the base shown. Then the other leg, the altitude of the triangle, is ...

  h = √((5√2)² - 2²) = √46

Then the area of the triangle shown is ...

  A = (1/2)bh = (1/2)(4)(√46)

  A = 2√46

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The area of the semicircle is given by the formula ...

  A = (1/2)πr²

Filling in the radius shown, the area is computed as ...

  A = (1/2)π(5√2/2)² = 25π/4

So, the total area of the figure is ...

  total area = triangle area + semicircle area

  = 2√46 + 25π/4 . . . square meters

  ≈ 33.2 . . . square meters

12/11c

or

12

c

11