The distance from the point of intersection of the diagonals of the rectangle ABCD

The distance from the point of intersection of the diagonals of the rectangle ABCD to its two sides is 4cm and 5cm. Find the area of the triangle AOD.

1. АС and ВD are diagonals. O is the point of their intersection. OE – perpendicular to the AD side. OK – perpendicular to the AB side. EO = 4 cm. KO = 5 cm.

2. Distances from point O to the sides of the rectangle are perpendiculars EO and KO.

3. Calculate the area (S) of the AKOE rectangle:

S = EO x KO = 5 x 5 = 20 cm².

4. Calculate the area (S) of the AOE triangle:

S = 20: 2 = 10 cm².

5. Triangle AOE is equal to triangle DOE. With this in mind, we calculate the area (S)

triangle AOD:

S = 10 x 2 = 20 cm².

Answer: the area of the triangle AOD is 20 cm².