Math Problem Statement

Find the area of the parallelogram where the base is 15 cm, the height is 9 cm, and the slanted side is 17 cm.

Solution

To calculate the area of this parallelogram, we use the formula for the area of a parallelogram:

Area=base×height\text{Area} = \text{base} \times \text{height}

From the image:

  • The base of the parallelogram is 15cm15 \, \text{cm} (the side adjacent to the height).
  • The height is 9cm9 \, \text{cm} (the perpendicular distance from the base).

Now, calculating the area:

Area=15cm×9cm=135cm2\text{Area} = 15 \, \text{cm} \times 9 \, \text{cm} = 135 \, \text{cm}^2

Thus, the area of the parallelogram is 135 cm².

Would you like a detailed explanation or have any questions? Here are some related questions to further expand on this:

  1. How do you find the area of a parallelogram if the height is not given?
  2. Can you find the area of a triangle if you know the base and height?
  3. What is the difference between finding the area of a rectangle and a parallelogram?
  4. How do you calculate the perimeter of a parallelogram?
  5. How can you find the height of a parallelogram if the area and base are known?

Tip: For any parallelogram, the height is always perpendicular to the base, even if it appears slanted.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area of Parallelograms

Formulas

Area = base × height

Theorems

Properties of Parallelograms

Suitable Grade Level

Grades 6-8