Instructions
Complete the following exercises using your knowledge of geometry concepts. Show your work for calculations and explanations where applicable!
1. Angles and Triangles
A triangle has two angles measuring 45 degrees and 55 degrees. Calculate the measure of the third angle.
2. Area of a Triangle
Find the area of a triangle with a base of 10 cm and a height of 5 cm.
3. The Pythagorean Theorem
In a right triangle, one leg measures 6 cm and the other leg measures 8 cm. Use the Pythagorean theorem to find the length of the hypotenuse.
4. Circles
Calculate the circumference of a circle with a radius of 7 cm. (Use π ≈ 3.14)
5. Volume of a Cylinder
A cylinder has a radius of 3 cm and a height of 10 cm. Calculate its volume. (Use the formula V = πr²h)
6. Quadrilaterals
Identify what type of quadrilateral is formed by the following four points: A(1, 2), B(5, 2), C(5, 4), D(1, 4). Explain your reasoning.
7. Coordinate Geometry
What is the distance between the points (2, 3) and (6, 7) in a coordinate plane? Use the distance formula: d = √[(x2 - x1)² + (y2 - y1)²].
8. Reflection
Explain what happens to a shape when it is reflected across the x-axis. Provide an example with coordinates of a shape and its reflection.
9. Surface Area of a Rectangular Prism
Find the surface area of a rectangular prism with length 4 cm, width 3 cm, and height 5 cm. (Use the formula SA = 2lw + 2lh + 2wh)
10. Fun Challenge
If you were to create a character in the style of One Piece, what geometric shape would they resemble and why? Draw a quick sketch of your character idea around the description.