Instructions
Complete the following questions related to geometry concepts. Show all your work in the spaces provided.
1. Angle Relationships
Two angles are supplementary if the sum of their measures is 180 degrees. If one angle measures 75 degrees, what is the measure of its supplementary angle?
Supplementary angle: ____________ degrees
2. Area of a Triangle
The area of a triangle can be calculated using the formula:
Area = 1/2 × base × height
If a triangle has a base of 10 cm and a height of 5 cm, what is its area?
Area: ____________ cm²
3. Pythagorean Theorem
In a right triangle, if one leg is 6 cm and the other leg is 8 cm, find the length of the hypotenuse using the Pythagorean theorem:
a² + b² = c²
Hypotenuse (c): ____________ cm
4. Circumference of a Circle
The circumference of a circle can be calculated using the formula:
C = 2 × π × r
If the radius of a circle is 4 cm, what is its circumference? (Use π ≈ 3.14)
Circumference: ____________ cm
5. Volume of a Rectangular Prism
The volume of a rectangular prism can be calculated using the formula:
Volume = length × width × height
If the length is 5 cm, the width is 3 cm, and the height is 4 cm, what is the volume?
Volume: ____________ cm³
6. Identify the Shapes
Draw a triangle, square, and a circle in the spaces below:
Triangle:
Square:
Circle:
7. Real-Life Application
A rectangular garden measures 10 m by 6 m. If you want to create a pathway that is 1 m wide all around the garden, what will be the area of the pathway?
Area of the pathway: ____________ m²
8. Challenge Problem
The sum of the interior angles of a triangle is 180 degrees. If one angle of the triangle is 40 degrees, and another angle is 70 degrees, what is the measure of the third angle?
Third angle: ____________ degrees