Composite Figures: Area Calculations

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Questions and Answers

Describe a strategy for designing a composite figure with an area of 200 square units using at least three distinct geometric shapes.

One strategy is to start with a rectangle of known area, then add or subtract areas using other shapes until the total area equals 200 square units.

Which of the following is NOT a necessary step when finding the area of a composite figure?

Finding the perimeter of each individual shape (correct)
Decomposing the figure into basic shapes
Finding the area of each individual shape
Adding all the areas together

The area of a semicircle is exactly half the area of a circle with the same radius.

True (A)

A composite figure consists of a square and an equilateral triangle attached to one of its sides. If the square has a side length of 6 cm, what additional information is needed to find the area of the composite figure?

The height of the triangle (C) Signup and view all the answers

The area of a rectangle with a length of 12 inches and a width of 8 inches is ______ square inches.

96 Signup and view all the answers

Match the composite figure with the correct method to calculate its area.

Rectangle with a triangle on top = Calculate the area of the rectangle and the triangle separately, then add them together. Circle with a square cut out of the center = Calculate the area of the circle and subtract the area of the square. Two overlapping rectangles = Calculate the area of each rectangle, add them, and subtract the overlapping area. Semicircle and a triangle = Calculate the area of the semicircle and the triangle separately, then add them together. Signup and view all the answers

What is the area of a semicircle with a diameter of 8 inches?

$8\pi$ square inches (C) Signup and view all the answers

Explain how knowing the formulas for basic shapes (e.g., rectangle, triangle, circle) is crucial for finding the area of composite figures.

Formulas for basic shapes are essential because composite figures are made up of these shapes. To find the total area, you need to calculate the individual areas using these formulas and then combine them. Signup and view all the answers

If a square and a circle have the same perimeter, the square will always have a larger area than the circle.

False (B) Signup and view all the answers

A composite shape is formed by a rectangle with dimensions 6 cm by 4 cm, and a right-angled triangle with a base of 4 cm and a height of 3 cm attached to one of the longer sides of the rectangle. What is the total area of the composite shape?

30 cm (A) Signup and view all the answers

To find the area of the composite shape shown (rectangle and semicircle), you need to calculate the area of the rectangle, calculate the area of the _______, then add them together.

semicircle Signup and view all the answers

A flag design consists of a large rectangle with a smaller triangle at the hoist side. If the rectangle is 5 feet wide and 3 feet tall, and the triangle has a base of 2 feet and a height of 3 feet, what is the total area of the flag?

18 square feet (B) Signup and view all the answers

Explain how to find the area of an L-shaped figure composed of two rectangles.

Divide the L-shape into two rectangles, calculate the area of each rectangle separately, and then add the two areas together to find the total area. Signup and view all the answers

When calculating the area of a composite figure, it is always necessary to subtract overlapping areas.

True (A) Signup and view all the answers

A circular garden with a diameter of 10 feet has a square sandbox placed in its center. If the sandbox has sides of 4 feet, what is the area of the garden excluding the sandbox?

$25\pi - 16$ square feet (C) Signup and view all the answers

A missing side length of a shape within a composite area can be found using the _______ theorem.

Pythagorean Signup and view all the answers

Match the shape with its respective area equation.

Circle = $\pi r^2$ Triangle = $0.5 \cdot b \cdot h$ Rectangle = $l \cdot w$ Trapezoid = $0.5 \cdot (a+b) \cdot h$ Signup and view all the answers

Which of the following composite figures would require subtracting areas to find the total area?

A circle with a square cut out of it (C) Signup and view all the answers

Describe how you would calculate the area of a figure shaped like a dartboard, which consists of concentric circles.

Calculate the area of each circle, then subtract the area of the inner circle from the next larger circle, continuing outwards to find the area of each ring. Finally, sum the areas of all the rings and the innermost circle. Signup and view all the answers

Doubling the radius of a semicircle will exactly double its area

False (B) Signup and view all the answers

Flashcards

What is a composite figure?

A figure made up of two or more simple geometric shapes.

What is circumference?

The distance around a circle.