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Unit 6: Area, Surface Area, and Volume Study Guide Directions: Complete all problems showing your work. Don' 1.) Find the total area of the figure shown.

Unit 66: Area, Surface Area, and Volume Study Guide\newlineDirections: Complete all problems showing your work. Don'\newline11.) Find the total area of the figure shown.

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Q. Unit 66: Area, Surface Area, and Volume Study Guide\newlineDirections: Complete all problems showing your work. Don'\newline11.) Find the total area of the figure shown.
  1. Identify Shapes: Identify the shapes that make up the figure. Let's say the figure is composed of a rectangle and a semicircle.
  2. Calculate Rectangle Area: Calculate the area of the rectangle. If the rectangle has a length of ll and a width of ww, the area is Arect=l×wA_{\text{rect}} = l \times w.
  3. Calculate Semicircle Area: Calculate the area of the semicircle. If the diameter of the semicircle is equal to the width of the rectangle ww, the radius rr is w2\frac{w}{2}. The area of a full circle is πr2\pi r^2, so the area of the semicircle is πr22=π(w2)22\frac{\pi r^2}{2} = \frac{\pi(\frac{w}{2})^2}{2}.
  4. Find Total Area: Add the areas of the rectangle and the semicircle to find the total area. Total Area = Arect+AsemicircleA_{\text{rect}} + A_{\text{semicircle}}.
  5. Calculate Total Area: Plug in the values for ll, ww, and π\pi (use π=3.14\pi = 3.14) to calculate the total area. Let's say l=10l = 10 units and w=6w = 6 units. So, Arect=10×6=60A_{\text{rect}} = 10 \times 6 = 60 square units and Asemicircle=(3.14×(62)2)/2=(3.14×32)/2=(3.14×9)/2=28.26/2=14.13A_{\text{semicircle}} = \left(3.14 \times \left(\frac{6}{2}\right)^2\right)/2 = \left(3.14 \times 3^2\right)/2 = \left(3.14 \times 9\right)/2 = 28.26/2 = 14.13 square units.
  6. Calculate Total Area: Plug in the values for ll, ww, and π\pi (use π=3.14\pi = 3.14) to calculate the total area. Let's say l=10l = 10 units and w=6w = 6 units. So, Arect=10×6=60A_{\text{rect}} = 10 \times 6 = 60 square units and Asemicircle=(3.14×(62)2)/2=(3.14×32)/2=(3.14×9)/2=28.26/2=14.13A_{\text{semicircle}} = \left(3.14 \times \left(\frac{6}{2}\right)^2\right)/2 = \left(3.14 \times 3^2\right)/2 = \left(3.14 \times 9\right)/2 = 28.26/2 = 14.13 square units. Add the areas together. Total Area = 60+14.13=74.1360 + 14.13 = 74.13 square units.

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