Final answer:
To find the area of quadrilateral ABCD, we can use the lengths of the sides and the formula for the area of a quadrilateral.
Step-by-step explanation:
To find the area of quadrilateral ABCD, we first need to determine the lengths of the sides. Since BM ⊥ AC and DN ⊥ AC, we can create right triangles by drawing lines from B and D perpendicular to AC. Using the Pythagorean theorem, we can find the lengths of BM and DN. BM is given as 4 cm, so we have:
BM^2 + MN^2 = BN^2
4^2 + MN^2 = 20^2
16 + MN^2 = 400
MN^2 = 400 - 16
MN^2 = 384
MN = √384 ≈ 19.6 cm
Similarly, DN is given as 4 cm, so we have:
DN^2 + NC^2 = DC^2
4^2 + NC^2 = 20^2
16 + NC^2 = 400
NC^2 = 400 - 16
NC^2 = 384
NC = √384 ≈ 19.6 cm
Now that we have the lengths of all four sides, we can use the formula for the area of a quadrilateral:
Area = 1/2 * (AC + BD) * (BM + DN)
Area = 1/2 * (20 + 19.6) * (4 + 4)
Area = 1/2 * 39.6 * 8
Area = 158.4 cm^2