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 = πr²
A = (3.14)[9cm - (2cm + 3 cm)]²
2
A = (3.14)[(9cm - 5 cm)]²
2
A = (3.14)(4cm)²
2
A = (3.14)(2cm)²
A = (3.14)(4 cm²)
A = (12.56 cm²)
A = 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 = (8.7 cm)(10 cm)(sin 60°) assuming that the triangle is equiangular
A = (8.7 cm)(10 cm)(0.3048106211)
A = (87 cm²)(0.3048106211)
A = (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.
