To find the area of a trapezoid, we need the lengths of the two bases (B¹ and B²) and the height (H). From the information given:
- We have three sides: 15 cm, 13 cm, and 9 cm.
- In a trapezoid, bases are typically the parallel sides.
Let's assume:
- \( B¹ = 15 , \text{cm} \) (one base)
- \( B² = 9 , \text{cm} \) (the other base)
- The third side, 13 cm, is a non-parallel side.
To find the height (H) of the trapezoid, we can use the formula for the area of a trapezoid, but first, we need to calculate the height. For this specific trapezoid configuration, we can make use of the Pythagorean theorem to find the height if we split the trapezoid into a rectangle and two right triangles.
Assuming the trapezoid is structured in such a way where the non-parallel sides are perpendicular to the bases, we can use:
- The distance between the bases as height (H).
- The difference of bases as a base of triangles on either side.
Let's calculate to find the height:
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The length of the bases:
- \( B¹ = 15 , \text{cm} \)
- \( B² = 9 , \text{cm} \)
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The difference between bases: \[ \text{Base Difference} = B¹ - B² = 15 , \text{cm} - 9 , \text{cm} = 6 , \text{cm} \] Let’s assume this 6 cm is divided equally on both sides since both non-parallel sides (assuming symmetry for simplicity).
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Thus, if we take the height perpendicular to the bases, we have: \[ \text{Height (H)} = \sqrt{13^2 - 3^2} = \sqrt{169 - 9} = \sqrt{160} \approx 12.65 , \text{cm} \] (We take half of 6 cm = 3 cm as the length of the triangle's base).
Now, we can calculate the area: \[ A = \frac{(B¹ + B²)}{2} \times H \] \[ A = \frac{(15 + 9)}{2} \times H \] \[ A = \frac{24}{2} \times 12.65 \] \[ A = 12 \times 12.65 \approx 151.8 , \text{cm}^2 \]
Thus, the approximate area of the trapezoid is: \[ A \approx 151.8 , \text{cm}^2 \]