Answer:
120
Step-by-step explanation:
The area of a rhombus is half of the product of the diagonals.
The vertical diagonal measures 2 * 5 = 10.
To find the length of the horizontal diagonal we need to do a calculation.
The diagonals of a rhombus are perpendicular, so each of the 4 triangles inside the rhombus is a right triangle.
Look at the upper left triangle.
The hypotenuse measures 13. One leg measures 5. We can use the Pythagorean theorem to find the length of the other leg.
a^2 + b^2 = c^2
a^2 + 5^2 = 13^2
a^2 + 25 = 169
a^2 = 144
a = 12
The horizontal leg is 12. The horizontal diagonal of the rhombus is twice that leg. 12 * 2 = 24
The diagonals of the rhombus measure 10 and 24.
area = diagonal1 * diagonal2/2
area = 10 * 24/2
area = 240/2
area = 120
