The SPA (Side, Perimeter, Area) method is a way of working with measurements to calculate perimeter and area in figures. In this case, let's analyze the provided shapes and use SPA to solve for any unknowns in the trapezoids shown.

Step 1: Identifying Given Information

1. The first trapezoid has a perimeter (P) of 117, but the area (A) is unknown. One of the side lengths appears to be 15.
2. The second trapezoid has an area (A) of 180, but the perimeter (P) is unknown. One of the side lengths is labeled as 4.

Step 2: Calculating Area and Perimeter of a Trapezoid

The formula for the area of a trapezoid is: $A = \frac{1}{2} \times (a + b) \times h$ where:

• $a$ and $b$ are the lengths of the two parallel sides,
• $h$ is the height.

The perimeter of a trapezoid is the sum of all its sides: $P = a + b + c + d$ where $a$, $b$, $c$, and $d$ are the lengths of each side.

Step 3: Solving for Unknowns Using Given Values

Since the image only partially shows dimensions, I’ll need more details about the lengths of other sides or heights to compute the exact values for the unknown areas and perimeters. If you can provide the missing measurements for each trapezoid, I can proceed with the calculations.

Would you like to share more measurements, or do you have specific questions about the process?

Related Questions:

1. How is the SPA method applied to trapezoids with known heights?
2. What’s the process for finding area when only perimeter is given?
3. How does changing one side impact the area and perimeter of a trapezoid?
4. Can we estimate unknown sides if we only know one side length and the perimeter?
5. How can we apply SPA to other quadrilaterals, like parallelograms?

Tip:

Always start by identifying and marking known measurements; this often simplifies the process for solving unknowns in geometry problems.