Question

What is the area of rectangle RSTU? Show step by step!

Answer 1

Step-by-step explanation:

We only know 1 side, and that is the width of 4. We only have the diagonals at our side. Half of the diagonal is 5. As a result, the diagonal is 10. I want you to imagine a triangle that has a base of 4 and a hypotenuse of 10. Use the Pythagorean Theorem to find b, or the height.

a² + b² = c²

4² + b² = 10²

16 + b² = 100

100 - 16 = 84

b² = 84

b = √84

b ≈ 9.165

Now we know the length of the rectangle, which is about 9.165. Multiply that by 4 to get the area.

9.165 * 4

36 + 0.4 + 0.24 + 0.020

36.4 + 0.24 + 0.02

36.64 + 0.02

36.66 u²

The area of rectangle RSTU is about 36.66 units squared.