area of a figure that is a rectangle diagonal 9 and angle 35round to nearest hundredth

Question

geometry help on homework please

Answer 1

When we draw a diagonal across the rectangle, we will have 2 congruent right triangles. The diagonal is the hypotenuse of the triangles.  The length and height are the legs.  What we need to do is find the length and height of the triangle, then multiply them.  Remember that we need the area of the rectangle, so we will NOT divide the length times height by 2.

 

Let's find the length and height of the triangle.  We can use basic trigonometric functions, since we have a right triangle.

 

 

Length = Diagonal × cosθ

           = 9cos35

           = 7.37

 

Height = Diagonal × sinθ

          = 9sin35

          = 5.16

 

 

The length is 7.37 and the height is 5.16. 

 

Let's use the Pythagorean theorem to verify these values.

 

(7.37)² + (5.16)² = 9²

54.32  + 26.63 = 81

81 = 81

 

The values are correct.

 

So,

 

Area = length × height

Area = 7.37  ×  5.16

Area = 38.03