When we draw out our picture and triangle, we should see that our angle is on the ground 70°, the height <em>x</em> is across from the angle and is the vertical leg up, and that our hypotenuse is equal to 6:

sin70° = x/6

6 0

3 years ago

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Please help! Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact valu

Nadya [2.5K]

Answer:

$The \ area \ of \ the \ figure = 4\dfrac{1}{2} \cdot \pi + 18 \ cm^2$

Step-by-step explanation:

Given that the figure is made up of portion of a square and a semicircle, we have;

BC ≅ AB = 6 cm

The area of semicircle BC with radius BC/2 = 3 is 1/2×π×r² = 1/2×π×3² = 4.5·π cm²

Triangle ABC = 1/2 × Area of square from which ABC is cut

The area of triangle ABC = 1/2×Base ×Height = 1/2×AB×BC = 1/2×6×6 = 18 cm²

The area of the figure = The area of semicircle BC + The area of triangle ABC

The area of the figure = 4.5·π cm² + 18 cm² = $\dfrac{9 \cdot \pi +36}{2} \ cm^2$ .

5 0

2 years ago