Question

How can you decompose the composite figure to determine its area? as a circle, three rectangles, and a triangle as a circle, a trapezoid, and four triangles as a semicircle, three rectangles, and a square as a semicircle, a trapezoid, and two rectangles.

Answer 1

The best way to decompose the composite figure to determine its area is as a semicircle, a trapezoid, and two rectangles. This way, we can use the following formulas to find the area of each part:

Area of a semicircle = 21​πr2, where r is the radius of the circle.

Area of a trapezoid = 21​(b1​+b2​)h, where b1​ and b2​ are the bases and h is the height of the trapezoid.

Area of a rectangle = l×w, where l is the length and w is the width of the rectangle.

Then, we can add up the areas of each part to find the total area of the composite figure. The other options are not as convenient because they either involve more parts or more complicated shapes. For example, option A would require finding the area of a triangle, which involves using trigonometry or the Pythagorean theorem. Option B would require finding the area of four triangles, which is more tedious than finding the area of two rectangles. Option C would require finding the area of a square, which is redundant because a square is a special case of a rectangle.

Explanation: