Math Problem Statement

Find the area of the shape below. Give your answer in m².

Solution

To solve the problem of finding the area of the given shape, we can break it into two parts:

  1. The rectangle: The rectangle is 15m×8m15 \, \text{m} \times 8 \, \text{m}. Area of the rectangle=15×8=120m2\text{Area of the rectangle} = 15 \times 8 = 120 \, \text{m}^2

  2. The triangle: The base of the triangle is 2315=8m23 - 15 = 8 \, \text{m}, and its height is 8m8 \, \text{m}. Area of the triangle=12×base×height=12×8×8=32m2\text{Area of the triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 8 = 32 \, \text{m}^2

Finally, adding the areas of the rectangle and the triangle: Total area=120+32=152m2\text{Total area} = 120 + 32 = 152 \, \text{m}^2

Answer:

The area of the shape is 152 m².

Would you like further clarification on any part of this solution? Here are 5 related questions to explore:

  1. How do you find the area of irregular shapes composed of more than two parts?
  2. What is the significance of breaking a complex figure into simpler shapes for area calculation?
  3. Can this problem be solved using other geometric methods?
  4. How does the formula for the area of a triangle change with different dimensions?
  5. What are practical applications of area calculation in real life?

Tip: Always label and break down complex shapes into basic geometric components for easier calculations.

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Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation
Composite Shapes

Formulas

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

Theorems

Basic area formulas for geometric shapes

Suitable Grade Level

Grades 6-8