https://r2.erweima.ai/mathbot/image/17264509675717gdtok46.jpg

The problem provided involves a rectangle with an area of 100 square units. It has dimensions of 5 (length) and 4 (width), and part of the rectangle is shaded in blue, forming a triangle. We are tasked with finding the area of this triangle.

### Step-by-step breakdown:

1. **Rectangle's Area**: 
   The rectangle has dimensions 5 (length) and 4 (width). The area of the rectangle is given by:
   \[
   \text{Area of rectangle} = 5 \times 4 = 20 \, \text{square units}
   \]
   However, the problem states that the area of the rectangle is 100 square units, which suggests either the provided area information is about the whole or the diagram's scale is different. For now, we'll proceed using the dimensions shown.

2. **Shaded Triangle**: 
   The shaded blue region forms a right triangle within the rectangle, with its hypotenuse extending from one corner of the rectangle to the opposite side. The base of the triangle appears to be the same as the length of the rectangle (5 units), and the height is the same as the width of the rectangle (4 units).

3. **Area of the Triangle**: 
   The formula for the area of a triangle is:
   \[
   \text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}
   \]
   Substituting the values for the base and height:
   \[
   \text{Area of triangle} = \frac{1}{2} \times 5 \times 4 = 10 \, \text{square units}
   \]

Thus, the area of the blue shaded triangle is **10 square units**.

Would you like more details or further clarifications?

---

Here are five related questions:
1. How would the area change if the dimensions of the rectangle doubled?
2. What if the triangle was not a right triangle? How would you calculate the area?
3. Could this method work for finding the area of other polygons inside a rectangle?
4. What happens to the triangle's area if we change its orientation inside the rectangle?
5. How would we compute the area if the triangle was inscribed in a circle instead of a rectangle?

**Tip**: When calculating the area of any triangle, identifying the base and height correctly is crucial to ensure accurate results.

This geometry problem involves calculating the area of a triangle inside a rectangle with given dimensions. Learn how to apply the formulas for the area of a rectangle and triangle to find the shaded area. Suitable for students in Grades 5-7.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation