Question: MATHTia Calculating Area of Composite Figures < Unit Overview Step-by-Step Sample Problem Hints…

MATHTia Calculating Area of Composite Figures

< Unit Overview Step-by-Step Sample Problem Hints

The given figure consists of a square and a triangle.

The base of triangle SQU is 9.4 inches and the height is 9.4 inches.

Use the given information to complete the worksheet.

Diagram Label Value Base of Triangle SQU Height of Triangle SQU Area of Triangle SQU Side of Square SUAR Area of Square SUAR

The area of the given figure is

Area Formulas:

• Parallelogram: \( A = bh \)
• Triangle: \( A = \frac{1}{2}bh \)

[Diagram of a square and a triangle] S E R A

Solution

The problem involves finding the areas of a square and a triangle that form a composite figure. Given: - Base of triangle SQU = 9.4 inches - Height of triangle SQU = 9.4 inches Use the given information to calculate the following: 1. Area of Triangle SQU The area of a triangle is given by: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] Substitute the given values: \[ \text{Area of Triangle SQU} = \frac{1}{2} \times 9.4 \times 9.4 = \frac{1}{2} \times 88.36 = 44.18 \text{ square inches} \] 2. Side of Square SUAR Since the problem involves a square, the side of the square SUAR is equal to the base of the triangle SQU. Therefore, \[ \text{Side of Square SUAR} = 9.4 \text{ inches} \] 3. Area of Square SUAR The area of a square is given by: \[ \text{Area} = \text{side} \times \text{side} \] Substitute the side length: \[ \text{Area of Square SUAR} = 9.4 \times 9.4 = 88.36 \text{ square inches} \] 4. Total Area of the Composite Figure The total area is the sum of the areas of the triangle and the square. \[ \text{Total Area} = \text{Area of Triangle SQU} + \text{Area of Square SUAR} \] \[ \text{Total Area} = 44.18 + 88.36 = 132.54 \text{ square inches} \] Thus, the area of the given figure is 132.54 square inches.