Math Problem Statement

What is the area of Figure I in the terrace diagram?

Solution

From the uploaded image, the terrace is divided into two figures:

  1. Figure I: A right triangle.
  2. Figure II: A rectangle.

To calculate the area of Figure I (triangle):

The formula for the area of a triangle is:

Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}

  • Base = 10ft10 \, \text{ft}
  • Height = 12ft12 \, \text{ft}

Substituting these values:

Area of Figure I=12×10×12=60square feet.\text{Area of Figure I} = \frac{1}{2} \times 10 \times 12 = 60 \, \text{square feet.}

The area of Figure I is 60 square feet.

Would you like help calculating the area of Figure II or answering further related questions? Let me know!


Follow-Up Questions:

  1. How do you calculate the area of the rectangle (Figure II)?
  2. What is the total area of the terrace?
  3. How would you tile the terrace efficiently?
  4. Can you explain how to solve for the hypotenuse of the triangle in Figure I?
  5. What if the dimensions changed—how would that affect the calculations?

Tip:

Always double-check units (e.g., feet, meters) and ensure consistent dimensions when calculating areas.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Area calculation
Properties of triangles

Formulas

Area of a triangle = (1/2) × base × height

Theorems

Basic properties of right triangles

Suitable Grade Level

Grades 6-8