Question

In rectangle ABCD, BC = 2AB. Points O and M are the midpoints of AD and

BC, respectively. Point P bisects AO. If OB = 6√2 units, what is the area of
ANOP?
A
P
O
D
N
B
M
C

Answer 1

To find the area of triangle ANOP, we used the fact that rectangle ABCD has sides in a 1:2 ratio and the length of diagonal OB to determine both AB and BC. Considering the midpoints, we find that triangle ANOP is a right triangle with an area of 2.25 square units.

Step-by-step explanation:

The question asks us to calculate the area of triangle ANOP in a rectangle where one side is double the length of the other and given the length of the diagonal OB.

Since rectangle ABCD has BC = 2AB and OB = 6√2 units, we can determine that AB (the width) is 6 units and BC (the length) is 12 units. Point O is the midpoint of AD, so AO is equal to half of AB, which means that AO is 3 units long. Point P bisects AO, making AP = 1.5 units. As a result, the triangle ANOP is a right triangle with a base (NP) of 1.5 units and a height (AO) of 3 units. The area of ANOP is then (1.5 * 3) / 2 = 2.25 square units.