Math Problem Statement

识别图片中的问题,并给出解答步骤

Solution

The problem statement translates to:

  1. In the given diagram, ABCDABCD is a parallelogram. BECEBE \perp CE, and intersects ADAD and CDCD at points FF and GG respectively. Given CE=9CE = 9 and BF=12BF = 12, find the area of the parallelogram ABCDABCD.

To solve this problem, we will follow these steps:

  1. Identify the relationships: Given BECEBE \perp CE, triangle BCEBCE is a right triangle with BEBE as the height and CECE as the base.
  2. Calculate area of BCE\triangle BCE: The area of a triangle is given by 12×base×height\frac{1}{2} \times \text{base} \times \text{height}. Here, base=CE=9\text{base} = CE = 9 and height=BE\text{height} = BE.
  3. Find BEBE: Using the given BF=12BF = 12 and knowing that BFBF is the perpendicular distance from BB to line ADAD, we realize that BE=BF=12BE = BF = 12 because both are heights from the same vertex to a parallel side (by the properties of a parallelogram).
  4. Calculate the area of BCE\triangle BCE: Area of BCE=12×9×12=54\text{Area of } \triangle BCE = \frac{1}{2} \times 9 \times 12 = 54
  5. Determine the area of the parallelogram: Since BEBE is the height from BB to ADAD, and the area of parallelogram ABCDABCD is twice the area of BCE\triangle BCE: Area of ABCD=2×Area of BCE=2×54=108\text{Area of } ABCD = 2 \times \text{Area of } \triangle BCE = 2 \times 54 = 108

Thus, the area of the parallelogram ABCDABCD is 108108 square units.

If you have any questions or need further details, please let me know.

Here are 5 questions you might want to ask next:

  1. How do you find the area of a parallelogram?
  2. What properties of a parallelogram are used in calculating its area?
  3. How does knowing the perpendicular height help in determining the area of a parallelogram?
  4. Can the area of a parallelogram be found using its diagonals?
  5. What are some common mistakes to avoid when calculating the area of a parallelogram?

Tip: When working with geometric shapes, always consider their properties and the relationships between different parts of the shape to simplify your calculations.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Area of Parallelograms
Properties of Parallelograms

Formulas

Area of a triangle: (1/2) * base * height
Area of a parallelogram: base * height

Theorems

Properties of parallelograms
Relationship between base, height, and area

Suitable Grade Level

Grades 9-12