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2 years ago

In each problem below, find the total area of the shaded regions. Thanks!

Mathematics

1 answer:

nika2105 [10]2 years ago

5 0

The area of the shaded region = area of semicircle - area of triangle ACB = 11.32 cm².

<h3>What is the Area of a Semi-circle and Triangle?</h3>

Area of a triangle = 1/2(base)(height).

Area of a semi-circle = 1/2(πr²).

m∠ACB is a right triangle based on the central angle theorem. Therefore, ΔACB is a right triangle.

Radius of circle = OC = 4 cm

CB = 4 cm

Diameter AB = 2(4) = 8 cm

Using the Pythagorean theorem, find AC in ΔACB:

AC = √(AB² - CB²)

AC = √(8² - 4²)

AC ≈ 6.9 cm

Area of ΔACB = 1/2(CB)(AC)

Area of ΔACB = 1/2(4)(6.9)

Area of ΔACB ≈ 13.8 cm²

Area of semicircle = 1/2(πr²) = 1/2(π)(4²)

Area of semicircle ≈ 25.12 cm²

Area of the shaded region = area of semicircle - area of triangle ACB = 25.12 - 13.8

Area of the shaded region = 11.32 cm²

Learn more about the area of semicircle and triangle on:

brainly.com/question/14711792

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3 years ago

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3 years ago

Ten less than half of a number(x) is 6.

Likurg_2 [28]

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Given the following data;

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3 years ago

What is the surface area of the triangular prism shown?

Lunna [17]

Answer:

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The second side that we are going to solve for is the bottom rectangle. We are given a width of 12 cm and a length of 25 cm so lets just multiply them against each other to get the area.

$Area = l * w$

$Area = 25\ cm * 12\ cm$

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The next area that we are going to determine is the back rectangle which has a width of 9 cm and a length of 25 cm so lets just multiply them against each other to get the area.

$Area = l * w$

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$Area = 225\ cm^2$

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