AREA OF COMPOSITE FIGURES

COMPOSITE FIGURES A composite figure is made of triangles, quadrilaterals, semicircles, and other 2-D figures. A semicircle is half of a circle. Examples: TRIANGLE RECTANGLE SEMICIRCLE TRAPEZOID To find the area of a composite figure, separate it into figures with areas you know how to find. Then add those areas.

BOTH AREAS ADDED TOGETHER: AREA OF COMPOSITE FIGURES Let’s find the area of the following composite figure. 6 cm This figure can be separated into a rectangle and a semicircle. Now we just find the area of each figure. 3 cm 14 cm AREA OF SEMICIRCLE: A =  r2 (this is area of a 2 circle, cut in ½) A = 3.14  4  4 2 A = 50.24 = 25.12 cm2 AREA OF RECTANGLE: A = lw A = 14  3 A = 42 cm2 BOTH AREAS ADDED TOGETHER: 42 + 25.12 = 67.12 cm2

AREA OF COMPOSITE FIGURES Now you try to find the area of the following composite figure. This figure can be separated into a triangle and ¾ of a circle. Now we just find the area of each figure. 3 cm Together: 18 + 21.195 = 39.195 cm2 for the area of the composite figure. 12 cm AREA OF CIRCLE: A =  r2 (this is area of a WHOLE circle) A = 3.14  3 3 A = 28.26 cm2 (WHOLE CIRCLE) Now, we only need area for 3 parts of the circle ; so we need to divide the area by 4 to get ¼ then multiply by 3 to get ¾. 28.26 ÷ 4 = 7.065. 7.065  3 = 21.195 cm2 is ¾ of circle. AREA OF TRIANGLE: A = bh 2 A = 12  3 A = 36 = 18 cm2

AREA OF COMPOSITE FIGURES Now you try again to find the area of the following composite figure. This figure can be separated into a square & a rectangle. Now we just find the area of each figure. 9 cm 6 cm 3 cm 12 cm AREA OF SQUARE: A = side  side A = 3  3 A = 9 cm2 AREA OF RECTANGLE: A = bh A = 12  3 A = 36 cm2 Together: 9 + 36 = 45 cm2 for the area of the composite figure.

Now, we take the 2 areas and subtract: AREA OF SHADED PARTS OF FIGURES Sometimes you have to find the area of the shaded region in each figure. This figure is a large circle with a small circle inside it. To find the area of just the shaded part (the outer circular part), we need to find the area of both the larger circle and the smaller white filled circle, and then subtract the two areas to get just the shaded circle’s area. 6 m 8 m AREA OF SMALL CIRCLE: A = r2 A = 3.14  3  3 A = 28.26 m2 AREA OF LARGE CIRCLE: A = r2 A = 3.14  4  4 A = 50.24 m2 Now, we take the 2 areas and subtract: 50.24 – 28.26 = 21.98 m2

Now, we take the 2 areas and subtract: AREA OF SHADED PARTS OF FIGURES Now you try This figure is a large circle inside a square. Find the area of only the rectangle part showing around the circle. 6 m 12 m AREA OF SQUARE: A = s2 A = 12  12 A = 144 m2 AREA OF CIRCLE: A = r2 A = 3.14  6  6 A = 113.04 m2 Now, we take the 2 areas and subtract: 144.00 – 113.04 = 30.96 m2