Math Problem Statement

Find the area of the shaded section

Find the area of the shaded section in the given diagram.

Solution

To find the area of the shaded section in the diagram, we can break it down into simpler geometric shapes. The figure seems to be composed of a rectangle at the bottom and a trapezium or triangular shape on top.

Step-by-step calculation:

  1. Bottom Rectangle (ABFG):

    • Length =12cm= 12 \, \text{cm} (from AA to GG).
    • Height =9cm= 9 \, \text{cm} (from AA to BB).

    Area of rectangle = length×height=12×9=108cm2\text{length} \times \text{height} = 12 \times 9 = 108 \, \text{cm}^2.

  2. Top Trapezium or Triangle (CDEF):

    • The base of the trapezium at the bottom is 12cm12 \, \text{cm} (from CC to FF).
    • The top length is 6+6=12cm6 + 6 = 12 \, \text{cm} (from CC to EE).
    • The total height of the trapezium is 18cm18 \, \text{cm} (from CC to DD) minus the height of the rectangle 9cm9 \, \text{cm}, so the height of the trapezium is 189=9cm18 - 9 = 9 \, \text{cm}.

    For a trapezium: Area=12×(Base1+Base2)×Height\text{Area} = \frac{1}{2} \times ( \text{Base}_1 + \text{Base}_2 ) \times \text{Height} Substituting the values: Area=12×(12+12)×9=12×24×9=108cm2\text{Area} = \frac{1}{2} \times (12 + 12) \times 9 = \frac{1}{2} \times 24 \times 9 = 108 \, \text{cm}^2

  3. Total Area of the Shaded Section: The shaded area consists of the rectangle and the trapezium on top. Adding the areas: Total Area=108cm2+108cm2=216cm2\text{Total Area} = 108 \, \text{cm}^2 + 108 \, \text{cm}^2 = 216 \, \text{cm}^2

Thus, the area of the shaded section is 216 cm².


Would you like further clarification on any step? Here are some related questions to explore:

  1. How do you find the area of a trapezium in general cases?
  2. What are other ways to divide complex shapes into simpler ones?
  3. What is the difference between finding the area of a triangle and a trapezium?
  4. How would the total area change if the dimensions of the rectangle were different?
  5. What is the formula for the area of a complex polygon?

Tip: Always try breaking down complex figures into simpler, known shapes to make area calculations easier.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation
Trapezium
Rectangle

Formulas

Area of rectangle = length × height
Area of trapezium = 1/2 × (Base1 + Base2) × height

Theorems

-

Suitable Grade Level

Grades 7-9