PLEASE HELP!! SHOW WORK! <3 Find the area of this figure. Dimensions are in meters.

Mathematics

1 answer:

densk [106]3 years ago

3 0

Answer:

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

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

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