Area of Complex Figures Worksheet
This worksheet focuses on calculating the area of complex geometric figures by decomposing them into simpler shapes like rectangles, triangles, and circles.
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Area of Complex Figures
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Read each problem carefully and calculate the area of the complex figures. Show all your work for full credit. Remember to break down complex shapes into simpler, recognizable geometric figures.
1. Find the area of the figure below, which consists of a rectangle and a semicircle. The rectangle has a length of 10 cm and a width of 6 cm. The semicircle is attached to one of the 6 cm sides.
2. A complex shape is formed by a square with side length 8 meters and an equilateral triangle attached to one of its sides. The area of the square is square meters, and the height of the equilateral triangle is meters. Therefore, the total area of the complex figure is square meters.
3. Which of the following formulas would be used to find the area of a figure composed of a trapezoid and a rectangle?
A = (1/2)(b1+b2)h + lw
A = πr² + lw
A = bh + (1/2)bh
A = s² + (1/2)ap
4. Calculate the area of the shaded region in the figure below, where a circle with a radius of 4 cm is inscribed within a square with a side length of 8 cm.
5. Match the complex figure description with the correct area calculation method.
a. Rectangle with a triangle on top
i. Subtract area of inner shape from outer shape
b. Square with a circular hole
ii. Add areas of two rectangles
c. L-shaped figure
iii. Add area of rectangle and area of triangle