Test questions: Calculating area of shapes involving semicircles for Grade 7.

📚 Quick Study Guide

• 📏 Understanding Area: Area is the amount of space inside a 2D shape.
• 🔴 Area of a Circle: The formula is $A = \pi r^2$, where $r$ is the radius.
• 🌗 Area of a Semicircle: A semicircle is half a circle, so its area is $\frac{1}{2} \pi r^2$.
• ➕ Combining Shapes: To find the area of a shape made of semicircles and other figures (like rectangles), calculate the area of each part separately and then add them together.
• 🔢 Remember $\pi$: Use 3.14 or $\frac{22}{7}$ as an approximation for $\pi$ unless your problem specifies otherwise.

Practice Quiz

1. What is the area of a semicircle with a radius of 7 cm?
   1. 38.5 $cm^2$
   2. 77 $cm^2$
   3. 154 $cm^2$
   4. 44 $cm^2$
2. A rectangle is 10 cm long and 5 cm wide. A semicircle with a diameter of 5 cm is attached to one of its shorter sides. What is the total area of the combined shape?
   1. 59.8125 $cm^2$
   2. 69.8125 $cm^2$
   3. 54.90625 $cm^2$
   4. 74.90625 $cm^2$
3. A shape consists of two semicircles, each with a radius of 3 cm, joined along their diameters. What is the total area of the shape?
   1. 14.13 $cm^2$
   2. 28.26 $cm^2$
   3. 56.52 $cm^2$
   4. 18.84 $cm^2$
4. A square has sides of length 8 cm. A semicircle is cut out from one side, with the side of the square as its diameter. What is the area of the remaining shape?
   1. 37.76 $cm^2$
   2. 49.76 $cm^2$
   3. 75.44 $cm^2$
   4. 25.12 $cm^2$
5. What is the diameter of a semicircle that has an area of 77 $cm^2$? (Use $\pi = \frac{22}{7}$)
   1. 7 cm
   2. 14 cm
   3. 21 cm
   4. 28 cm
6. A window is shaped like a rectangle topped by a semicircle. The rectangle is 4 ft wide and 6 ft high. What is the area of the window?
   1. 24 $ft^2$
   2. 24 + 6.28 $ft^2$
   3. 24 + 12.56 $ft^2$
   4. 36.56 $ft^2$
7. If you have a full circle area of $50.24 cm^2$, what would be the area of the semicircle formed from the same circle?
   1. 100.48 $cm^2$
   2. 25.12 $cm^2$
   3. 12.56 $cm^2$
   4. 75.36 $cm^2$