The area of ABED is 49 square units. Given AGequals9 units and ACequals10 units, what fraction of the area of ACIG is represent

Question

svetlana

3 months ago

5

The area of ABED is 49 square units. Given AGequals9 units and ACequals10 units, what fraction of the area of ACIG is represent

ed by the shaded region?

Mathematics

1 answer:

Svet_ta [12.7K] · Answer 1 · 2026-02-26T05:30:00+03:00

Answer:

The shaped region accounts for 7/18 of the area of ACIG.

Step-by-step explanation:

Refer to the attached diagram for further clarity on the problem.

Step 1

Determine the length of one side of square ABED.

We know that

AB=BE=ED=AD

The area of a square can be calculated as

$A=b^{2}$

where b is the side length.

We have

$A=49\ units^2$

So we substitute

$49=b^{2}$

$b=7\ units$

Thus,

$AB=BE=ED=AD=7\ units$

Step 2

Calculate the area of ACIG.

The area of rectangle ACIG is determined by

$A=(AC)(AG)$

Substituting the given values yields

$A=(9)(10)=90\ units^2$

Step 3

Determine the area of the shaded rectangle DEHG.

The area of rectangle DEHG is given by

$A=(DE)(DG)$

We find $DE=7\ units$

$DG=AG-AD=9-7=2\ units$

and substitute $A=(7)(2)=14\ units^2$

Step 4

Calculate the area of shaded rectangle BCFE.

The area of rectangle BCFE equals

$A=(EF)(CF)$

We see that

$EF=AC-AB=10-7=3\ units$

$CF=BE=7\ units$

and substitute

$A=(3)(7)=21\ units^2$

Step 5

Add the areas of the shaded regions together.

$14+21=35\ units^2$

Step 6

Divide the area of the shaded region by the area of ACIG.

$\frac{35}{90}$

Simplify this fraction by dividing both the numerator and denominator by 5.

$\frac{7}{18}$

Hence, the shaped region represents 7/18 of the area of ACIG.

The area of ABED is 49 square units. Given AGequals9 units and ACequals10 ​units, what fraction of the area of ACIG is represent

The area of ABED is 49 square units. Given AGequals9 units and ACequals10 units, what fraction of the area of ACIG is represent