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Geometric figure composed of two right triangles sharing a common side, labeled with dimensions 8m, 10m, and 17m.

$Right triangle PQS and triangle QSR forming a composite shape with side lengths 8m, 10m, and 17m, with right angles at Q and S.$

Right triangle PQS and triangle QSR forming a composite shape with side lengths 8m, 10m, and 17m, with right angles at Q and S.

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Show Answer Key & Explanations Step-by-step solution for: 15 Pythagorean Theorem Practice Problems For 8th Grade

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- The figure is a trapezoid PQRS with bases PQ = 8 m and SR = 17 m.
- The height of the trapezoid is QS, which is perpendicular to both bases.
- In triangle PQS, angle at Q is 90 degrees, so it is a right triangle with hypotenuse PS = 10 m and leg PQ = 8 m.
- Use the Pythagorean theorem to find QS: QS² = PS² - PQ² = 10² - 8² = 100 - 64 = 36.
- Therefore, QS = √36 = 6 m.
- The area of a trapezoid is given by: Area = (1/2) × (sum of bases) × height.
- Substitute the values: Area = (1/2) × (8 + 17) × 6 = (1/2) × 25 × 6 = 25 × 3 = 75 m².

Parent Tip: Review the logic above to help your child master the concept of pythagorean theorem math problems.

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$How to Use the Pythagorean Theorem. Step By Step Examples and Practice$