Math Problem Statement

Area of the following pentagon ABCDE is:

Solution

To calculate the area of the given pentagon ABCDEABCDE, we can break it down into two parts:

  1. Rectangle ABCDABCD:

    • The rectangle has a width of 8cm8 \, \text{cm} and a height of 8cm8 \, \text{cm}.
    • Area of ABCD=width×height=8×8=64cm2ABCD = \text{width} \times \text{height} = 8 \times 8 = 64 \, \text{cm}^2.
  2. Triangle ADEADE:

    • The triangle is isosceles, with a base AE=8cmAE = 8 \, \text{cm} and height DE=8cmDE = 8 \, \text{cm}.
    • Area of the triangle ADE=12×base×height=12×8×8=32cm2ADE = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 8 = 32 \, \text{cm}^2.

Total Area of the Pentagon:

Total Area=Area of Rectangle+Area of Triangle=64+32=96cm2\text{Total Area} = \text{Area of Rectangle} + \text{Area of Triangle} = 64 + 32 = 96 \, \text{cm}^2

Thus, the correct answer is:

(1) 96 cm²


Do you want further details or explanations? Here are some related questions to expand your understanding:

  1. How do we calculate the area of complex shapes systematically?
  2. What are the properties of an isosceles triangle?
  3. How is the height of a triangle used in area calculations?
  4. Can irregular polygons be divided into standard geometric shapes for area calculations?
  5. How does the Pythagorean theorem apply to finding unknown dimensions in geometry?

Tip: When solving problems involving composite shapes, always divide them into simpler components like triangles, rectangles, or circles for easier calculations.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation
Composite Shapes

Formulas

Area of rectangle = length × width
Area of triangle = 1/2 × base × height

Theorems

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Suitable Grade Level

Grades 6-8