Question

In the diagram below, DR is perpendicular to OP.

O
10.0
3.75
ok 4.0
M
Find the area of ADUO.
If entering your answer as a decimal, round your final answer to the nearest hundredth.
square units

Answer 1

Answer: the answer is 84. Just did it on khan academy the person before me is right

Explanation:

Answer 2

`A=84.00\ units^2`

Explanation:

step 1

Find the length side MU (height of triangle DUO)

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional

In this problem

Triangle DMU is similar to Triangle DPA by AA Similarity Theorem

because

∠DMU=∠DPA

∠MDU=∠PDA

Applying proportion

`(DM)/(DP)=(MU)/(PA)`

substitute the given values

`(10.0)/(3.75)=(MU)/(4.5)`

solve for MU

`MU=(10.0)/(3.75)(4.5)`

`MU=12\ units`

step 2

Find the area of triangle DUO

`A=(1)/(2) (OD)(MU)`

substitute

`A=(1)/(2) (4.0+10.0)(12)`

`A=84.00\ units^2`