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.

   Noah draws a right triangle on grid paper, legs 1 cm and 4 cm, then the square on its hypotenuse. That square comes out tilted. What is its area, in square cm?

   17
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.

   Zee measures a right-triangle corner of the school garden for square herb beds, one on each side. What is the area of the bed on the hypotenuse, in square meters?

   2.25
4. 4.

   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
5. 5.

   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
6. 6.

   Kira cut three paper squares to fit the sides of a right triangle and then lost a label. What is the area of the unlabeled square, in square cm?

   81
7. 7.

   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
8. 8.

   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
9. 9.

   Noah's math book labels a right triangle with letters. Which equation is true for the squares on its sides?

   • d + f = g
   • f² + g² = d²
   • d² + g² = f²
   • d² + f² = g²
10. 10.

    Ren's book shows a right triangle turned on its side, labeled with letters. Which equation is true for the squares on its sides?

    • w + y = v
    • w² + y² = v²
    • w² + v² = y²
    • y² + v² = w²