The angles between the diagonals of a rectangle is 30 degrees and each diagonal is 12 cm long. Find the area of the rectangle.

Guest Dec 29, 2014

#1**+10 **

Draw a picture of this rectangle with its diagonals.

This picture contains four triangles. You know that two sides of each of these interior triangles are each 6 cm long. In two of the triangles, the angle contained between these sides is 30° and in the other two triangles, the angle is 150°.

One formula for the area of a triangle is: Area = ½ · a · b · sin(C) Where a and b are the lengths of the two sides that contain ∠C.

So the area of two of the triangles is each: Area = ½ · 6 · 6 · sin(30°)

while the area of each of the other two triangles is: Area = ½ · 6 · 6 · sin(150°)

Add these four triangular areas to get the area of the rectangle.

geno3141
Dec 29, 2014

#1**+10 **

Best Answer

Draw a picture of this rectangle with its diagonals.

This picture contains four triangles. You know that two sides of each of these interior triangles are each 6 cm long. In two of the triangles, the angle contained between these sides is 30° and in the other two triangles, the angle is 150°.

One formula for the area of a triangle is: Area = ½ · a · b · sin(C) Where a and b are the lengths of the two sides that contain ∠C.

So the area of two of the triangles is each: Area = ½ · 6 · 6 · sin(30°)

while the area of each of the other two triangles is: Area = ½ · 6 · 6 · sin(150°)

Add these four triangular areas to get the area of the rectangle.

geno3141
Dec 29, 2014