Why a² + b² = c²: squares on the sides

Answer Key - Grade 8 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Pia sketches a right triangle on grid paper with legs 2 cm and 5 cm. The square on its hypotenuse is tilted. What is that square's area, in square cm?

   29
2. 2.

   Ren's puzzle card shows a tilted square on the hypotenuse of a right triangle with legs 3 cm and 5 cm. What is the tilted square's area, in square cm?

   34
3. 3.

   Tala's robot draws a right triangle on grid paper, legs 2 cm and 7 cm, and a tilted square on its hypotenuse. What is that square's area, in square cm?

   53
4. 4.

   Ari measures a right-triangle corner of the schoolyard for square flower beds, one on each side. What is the area of the bed on the hypotenuse, in square meters?

   6.25
5. 5.

   Bo measures a right-triangle sunflower plot with a square bed on each side. What is the area of the bed on the hypotenuse, in square meters?

   42.25
6. 6.

   Esme measures a right-triangle tile design with a square of tiles on each side. What is the area of the tile square on the hypotenuse, in square meters?

   1.69
7. 7.

   Not to scale. Jun has three paper squares that fit the sides of a right triangle. Two of them are labeled. What is the area of the unlabeled square, in square cm?

   64
8. 8.

   Luz's quilt has square patches on the three sides of a right-triangle patch. One label fell off. What is the area of the unlabeled patch, in square inches?

   45
9. 9.

   Milo's garden has square beds on the three sides of a right-triangle lawn. One sign is missing. What is the area of the unlabeled bed, in square feet?

   36
10. 10.

    Pia labels the sides of a right triangle q, s and u in pencil. Which equation is true for the squares on its sides?

    • q + s = u
    • q² + u² = s²
    • s² + u² = q²
    • q² + s² = u²