Instructions
Complete the following exercises related to geometry concepts. Show your work for each problem and provide explanations where necessary.
1. Angles in a Triangle
In a triangle, the measures of the angles are in the ratio of 2:3:4. What are the measures of the three angles?
2. Area of a Circle
Calculate the area of a circle with a radius of 7 cm. Use the formula A = πr² (use π ≈ 3.14).
3. Pythagorean Theorem
If one leg of a right triangle is 6 cm, and the other leg is 8 cm, what is the length of the hypotenuse? Use the formula a² + b² = c².
4. Surface Area of a Rectangular Prism
A rectangular prism has dimensions of 4 cm, 5 cm, and 10 cm. What is the surface area? Use the formula SA = 2(lw + lh + wh).
5. Volume of a Cylinder
Find the volume of a cylinder with a radius of 3 cm and a height of 10 cm. Use the formula V = πr²h.
6. Coordinate Geometry
Plot the points A(2, 3), B(5, 7), and C(3, 5) on the coordinate plane below. Then find the distance between points A and B.
Distance AB:
7. Word Problem
A rectangular garden measures 12 m by 15 m. If you want to add a path that is 1 m wide around the garden, what will be the area of the path?
8. Challenge Problem
If a square has a perimeter of 32 cm, what is the area of the square?
Reflection
What geometry concepts do you find most interesting, and why? Write your thoughts below: