How do you find the area of a compound figure

It depends on the figure.

Step-by-step explanation:

The compound figures we're generally concerned with are combinations of rectangles, triangles, circles or parts of circles, with or without cutouts of those shapes. The area is the sum of the areas of the component shapes, less the areas of any cutouts.

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Consider the attached examples:

7) This is half a circle together with two triangles. Or, the two triangles can be considered to be a rectangle with a triangular cutout.

The area is the sum of the areas of the semicircle and the rectangle, less the area of the triangular cutout.

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8) This can be considered as a square with a square cutout. The area is the difference between the area of the larger square and the area of the smaller one. Alternatively, one can find the area by finding the length of the centerline of the shaded area and multiplying that by the width of the shaded area.

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9) The area of this figure can be considered to be the total of the area of the bottom rectangle and the top triangle. Alternatively, one can cut the figure into two trapezoids (with a vertical line) and sum their areas.