---**Textual Information:** * **Other Relevant Text:** * Numbers labeling sides/height: 17, 20, 15, 15 (green), 20 (green). * Caption below image: SAT数学经典题型破解 (上) SAT如何高效备考? 专业SAT家教 ... 访问 > **Chart/Diagram Description:** * **Type:** Geometric figure (Trapezoid, likely a right trapezoid). * **Main Elements:** * A four-sided figure is shown, resembling a trapezoid. * The figure has a top horizontal side with length labeled as 20. * It has a right vertical side with length labeled as 15. * It has a bottom horizontal side with length labeled as 20 (in green text). * It has a left slanted side with length labeled as 17. * A dashed blue vertical line is drawn from the top left vertex perpendicular to the bottom base. This line represents the height. * The dashed blue line (height) is labeled with green text "15". * A red square symbol at the bottom of the dashed blue line indicates a right angle between the height and the bottom base. * Implicitly, there is a right angle at the bottom right corner due to the vertical right side and horizontal bottom base. * Green curved lines/arcs are present near the vertices but are not clearly defined.

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This diagram shows a trapezoid ABCD. The top base AB is 20 units, and the bottom base DC is also 20 units, shown in green. The right side BC is 15 units, while the left side AD is 17 units. A dashed blue line represents the height from point A to point E, which is 15 units, also shown in green. There are right angles at points C and E. This is a special case where both the top and bottom bases have equal lengths, making this a right trapezoid with parallel horizontal sides. Now let's calculate the area of this trapezoid. For a trapezoid, the area equals one-half times the height times the sum of the parallel sides. In our case, the height is 15 units, and both the top and bottom bases are 20 units. We can divide the trapezoid into two equal parts by drawing a line through the middle. Since both bases are equal, this is actually a special case where the trapezoid can be viewed as a rectangle with area equal to the height times the base. Substituting our values into the formula, we get one-half times 15 times the sum of 20 plus 20, which equals one-half times 15 times 40, giving us an area of 300 square units. Let's examine the left side of the trapezoid using the Pythagorean theorem. Looking at triangle ADE, we have a right angle at E. The vertical side AE is the height, which is 15 units. The horizontal distance DE is the difference between the x-coordinates of points D and E, which is 1 unit. According to the Pythagorean theorem, the square of the hypotenuse AD equals the sum of the squares of the other two sides. So AD squared equals 1 squared plus 15 squared, which is 1 plus 225, giving us 226. Taking the square root, we get approximately 15.03 units. However, the diagram shows AD as 17 units. This discrepancy suggests either a measurement error or that the trapezoid is not drawn to scale. In a perfectly accurate diagram, the left side should be approximately 15.03 units if the height is exactly 15 units and the horizontal distance is exactly 1 unit. Now let's calculate the perimeter of the trapezoid. The perimeter is the sum of all four sides. Starting from the top left vertex A and moving clockwise, we have: side AB equals 20 units, side BC equals 15 units, side CD equals 20 units, and side DA equals 17 units. Adding these values, we get a total perimeter of 72 units. This trapezoid has several interesting properties: it has equal parallel sides of 20 units each, a right angle at vertex C, an area of 300 square units as we calculated earlier, and a perimeter of 72 units. These measurements make it a special case of a right trapezoid with equal parallel sides. To summarize what we've learned about this trapezoid: First, it has equal parallel sides of 20 units each, making it a special case of a trapezoid. Second, the height is 15 units and forms a right angle with the base. Third, we calculated the area to be 300 square units using the formula one-half times height times the sum of the parallel sides. Fourth, the perimeter is 72 units, found by adding all four sides. Finally, we noticed a discrepancy with the left side measurement of 17 units, which doesn't match our Pythagorean theorem calculation of approximately 15.03 units. This suggests either a measurement error or that the diagram is not drawn precisely to scale. Understanding these properties is essential for solving SAT math problems involving geometric figures.