1. Descibe, using words and symbols, the relationship among the areas of the three squares shown.
The sum of the areas of the two smaller squares is equal to the area of the largest square.
6. a) Write an addition statement using the areas of these three squares.
b) What is the side length of each square?
c) Describe, using words and symbols, the relationship between the side lengths of each square.
a) 25cm²+144cm²= 169cm²
b) √25cm²= 5cm
c) The sum of the areas of the two smaller squares is equal to the area of the largest square.
a² + b²= c²
5² + 12²= 13²
13. A small triangular flower bed has a square stepping stone at each of its sides. Is the flower bed in the shape of a right triangle? Explain your reasoning.
4800cm²+4800cm²= 9600cm² not 9800cm²
No, the shape of the flower bed is not a right triangle because the sum of the areas of the two small squares does not equal the area of the largest square.
20. A right triangle has sides of 3cm, 4cm, and 5cm. Attached to each side is a semi-circle instead of a square. Describe the relationship between the areas of the semi-circles.
╥ x r²= area of a circle
3 ÷ 2= 1.5
3.14 x 2.25= 7.065
4 ÷ 2= 2
3.14 x 4= 12.56
5 ÷ 2= 2.5
3.14 x 6.25= 19.625
7.065 ÷ 2= 3.5325
12.56 ÷ 2= 6.28
19.625 ÷ 2= 9.8125
3.5325 + 6.28= 9.8125
The sum of the areas of the two smaller semi-circles is equal to the area of the largest semi-circle.
Here's a link to learn more about The Pythagorean Theorem.