1. The lengths of the bases of an isosceles trapezoid are in the ratio $7: 3$, and the leg is $2 \mathrm{~cm}$ longer than the height. Calculate the area of the trapezoid if the longer base is $21 \mathrm{~cm}$. Draw a sketch.
1. From the ratio of the lengths of the bases $7: 3=21: x$ we get the length of the shorter base, which measures $9 \mathrm{~cm}$. To calculate the height, we use the Pythagorean theorem $v^{2}=b^{2}-\left(\frac{a-c}{2}\right)^{2}$. We consider that $b=v+2$, substitute into the Pythagorean theorem, and calculate the length of the height, which is $8 \mathrm{~cm}$. The area of the trapezoid is $120 \mathrm{~cm}^{2}$.

![](https://cdn.mathpix.com/cropped/2024_06_07_2b0bf3255e176946d93cg-09.jpg?height=62&width=1642&top_left_y=817&top_left_x=204)

The appropriate sketch....................................................................................................................................

![](https://cdn.mathpix.com/cropped/2024_06_07_2b0bf3255e176946d93cg-09.jpg?height=54&width=1639&top_left_y=915&top_left_x=206)

![](https://cdn.mathpix.com/cropped/2024_06_07_2b0bf3255e176946d93cg-09.jpg?height=60&width=1639&top_left_y=964&top_left_x=206)

![](https://cdn.mathpix.com/cropped/2024_06_07_2b0bf3255e176946d93cg-09.jpg?height=48&width=1639&top_left_y=1021&top_left_x=206)

![](https://cdn.mathpix.com/cropped/2024_06_07_2b0bf3255e176946d93cg-09.jpg?height=51&width=1639&top_left_y=1071&top_left_x=206)