Use the Illustration below to solve the problem. The circles represent the 14 heads. Distribute the 40 legs to answer the problem. Consider the number of legs of goats and ducks in distributing the legs, O O O O ОО
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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 = 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.
What are the area formulas: brainly.ph/question/1836692
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