Answer:

Learning Task 1

2,657 cm²

69.28 cm²

9.26 cm²

Solutions:

1. Given: circle with r = 30 cm

4 - sided figure with s = 13 cm

First, find the area of the circle.

A = πr²

A = (3.14)(30 cm)²

A = (3.14)(900 cm²)

A = 2,826 cm²

Therefore, the area of the circle is 2,826 cm².

Next, find the area of the 4 - sided figure.

A = s²

A = (13 cm)²

A = 169 cm²

Subtract the area of the 4 - sided figure from the area of the circle.

Area of the Circle - Area of the 4 - sided figure

2,826 cm² - 169 cm² = 2,657 cm²

Therefore, the area of the circle that was not painted is 2, 657 cm².

2. Given: rectangle with dimensions 9 cm x 7 cm

semi - circle with diameter 9 cm - (2 cm + 3 cm)

Solve first for the area of the rectangle.

A = l x w

A = 9 cm x 7 cm

A = 63 cm²

Therefore, the area of the rectangle is 63 cm².

Next, solve for the area of the semi - circle.

A = \frac{1}{2}

2

1

πr²

A = \frac{1}{2}

2

1

(3.14)[9cm - (2cm + 3 cm)]²

2

A = \frac{1}{2}

2

1

(3.14)[(9cm - 5 cm)]²

2

A = \frac{1}{2}

2

1

(3.14)(4cm)²

2

A = \frac{1}{2}

2

1

(3.14)(2cm)²

A = \frac{1}{2}

2

1

(3.14)(4 cm²)

A = \frac{1}{2}

2

1

(12.56 cm²)

A = \frac{12.56}{2}

2

12.56

cm²

A = 6.28 cm²

Therefore, the area of the semi - circle is 6.28 cm².

Add the areas of the two figures.

Area of the rectangle + Area of the semi - circle

63 cm² + 6.28 cm² = 69.28 cm²

Therefore, the area of the given figure is 69.28 cm².

3. Given: scalene triangle with sides 8.7 cm and 10 cm

square with dimensions 2 cm x 2 cm

First, find the area of the triangle

A = \frac{1}{2}

2

1

(8.7 cm)(10 cm)(sin 60°) assuming that the triangle is equiangular

A = \frac{1}{2}

2

1

(8.7 cm)(10 cm)(0.3048106211)

A = \frac{1}{2}

2

1

(87 cm²)(0.3048106211)

A = \frac{1}{2}

2

1

(26.52 cm²)

A = 13.26 cm²

Next, find the area of the square.

A = s²

A = (2 cm)²

A = 4 cm²

Subtract the area of the square from the area of the scalene triangle.

Area of the scalene triangle - Area of the square

13.26 cm² - 4 cm² = 9.26 cm²

Therefore, the area of the shaded region is 9.26 cm².

What are the area formulas: brainly.ph/question/1836692

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