Which gives the area of a rhombus with sides of length 10 in. and longer diagonal of length 16 in.?
A 80 in.2
B 96 in.2
C 160 in.2
D 192 in.2

B

Explanation:

Draw the Rhombus

Draw a rhombus.

At the midpoint of the given diagonal, draw a line to the enclosed angle of two of the sides.

The diagonals meet at 90 degrees.

You can use the Pythagorean Theorem to get the third side.

c^2 = a^2 + b^2

c = 10                  length of 1 side

b = 8                   This is 1/2 of 16. They diagonals meet at their midpoints

a = ?

10^2 = 8^2 + a^2

100 = 64 + a^2

a^2 = 36

a = 6

The area of one right triangle = 6*8/2 = 24

The area of all 4 right triangles = 96