Solved examples: identifying base and height in parallelograms with pictures.

📚 Quick Study Guide

• 📐 A parallelogram is a four-sided shape (quadrilateral) with two pairs of parallel sides.
• 📏 The base of a parallelogram is any of its sides. Usually, we consider the bottom side as the base.
• 📈 The height is the perpendicular distance from the base to the opposite side. It's crucial that the height forms a right angle ($90^{\circ}$) with the base.
• ✏️ The area of a parallelogram is calculated using the formula: $Area = base \times height$.
• 💡 Note: The height is NOT the same as the length of the non-base side unless the parallelogram is a rectangle or square.

🧪 Practice Quiz

1. Which of the following statements correctly identifies the base and height in a parallelogram?

   1. A) The base is always the longest side, and the height is any other side.
   2. B) The base is any side, and the height is the perpendicular distance to the opposite side.
   3. C) The base is always the bottom side, and the height is the length of the adjacent side.
   4. D) The base and height are always equal in length.

2. In a parallelogram, if the base is 10 cm and the height is 5 cm, what is the area?

   1. A) 15 cm²
   2. B) 25 cm²
   3. C) 50 cm²
   4. D) 100 cm²

3. Which line represents the height of the parallelogram, given that the bottom side is the base?

   1. A) A diagonal line from one vertex to the opposite vertex.
   2. B) The side adjacent to the base.
   3. C) A line segment from the base forming a 90-degree angle to the opposite side.
   4. D) The longest side of the parallelogram.

4. If the area of a parallelogram is 48 cm² and the base is 8 cm, what is the height?

   1. A) 4 cm
   2. B) 6 cm
   3. C) 8 cm
   4. D) 12 cm

5. Which of these shapes is NOT a parallelogram?

   1. A) Square
   2. B) Rectangle
   3. C) Trapezoid
   4. D) Rhombus

6. In a parallelogram, if the acute angle between the base and the adjacent side is 60 degrees, can you directly use the length of the adjacent side as the height?

   1. A) Yes, the adjacent side is always the height.
   2. B) No, you need to find the perpendicular distance to calculate the height.
   3. C) Only if the adjacent side is equal to the base.
   4. D) Only if the parallelogram is a rhombus.

7. A parallelogram has a base of 12 cm and a height of 6 cm. What is its area?

   1. A) 18 cm²
   2. B) 36 cm²
   3. C) 72 cm²
   4. D) 144 cm²