Explanation:
so, I understand this is a rhombus, yes ?
I will base my answer on that assumption.
the area of a rhombus is
p×q/2
p, q being the diagonals.
so, all 4 sides are equally long (5 cm).
the angle(s) between the diagonals is (are) 90°.
opposing angles are equally sized (B = D, A = C), and they are split in half by the diagonals.
and always remember : the sum of all angles in a triangle is always 180°.
so,
b1 = b2 = d1 = 50°.
a1 = a2 = c1 = c2 = 180 - 90 - 50 = 40°.
law of cosine :
c² = a² + b² - 2ab×cos(C)
with c being the side opposite of angle C. a, b are the kthe 2 sides.
that applies to all 3 sides and angles.
BD² = 5² + 5² - 2×5×5×cos(c1 + c2) =
= 25 + 25 - 50×cos(80) = 50 - 50×cos(80) =
= 41.31759112....
BD = 6.427876097... cm ≈ 6.43 cm
AC² = 5² + 5² - 2×5×5×cos(b1 + b2) =
= 25 + 25 - 50×cos(100) = 50 - 50×cos(100) =
= 58.68240888...
AC = 7.660444431... cm ≈ 7.66 cm
the area of ABCD is a described
AC × BD / 2 = 24.62019383... cm² ≈ 24.62 cm²