SAT High School

Can you help me find area of the shaded region?

Answers

Answer 1

Answer:

Explanation:

Step One

The very first step is to show that triangles ΔABC, ΔFDC and ΔGEC are similar to one another.

1. All three triangles have a right angle in them.

ΔABC has a right angle at AΔFDE has a right angle at <FDEΔGEC has a right angle at <GEC

2. All three triangles have a common angle at C

3. All three triangles are similar by AA

Step Two

Find the ratios of the heights to one another.

AC / DC = 3/2

AB / DF = 3/2 The sides of similar triangles are in the same ratio.

Step Three

Find the area of ΔABC

Area ΔABC = 1/2 AB * AC

Area ΔABC = 81

Step Four

Find the Area of ΔDFC

Area of ΔDFC = 1/2 DF * DC

But DF and DC are known in terms of AB and AC

Area of ADC = 1/2 * 2/3 * AB * 2/3 * AC

Area of ADC = 1/2 * 4/9 * AB * AC

However 1/2 AB * AC = 81 so

Area ADC = 4/9 * 81 = 36

That's a very long complex step. Make sure you follow it through.

Step Five

Find the area of ΔGEC

By a similar process

EC = 1/3 AC

EG = 1/3 AB

Area ΔGEC = 1/2 * EC * EG

Area ΔGEC = 1/2 * 1/3 AC * 1/3 AB

Area ΔGEC = 1/2 * 1/9 * AB * AC

But 1/2 AB * AC = 81

Area ΔGEC = 1/9 * 81 = 9

Last Step

Find the area of the shaded area

ΔFDC - ΔGEC = Shaded area

36 -9 = 27 = shaded area

Related Questions

A partially filled pool contains 600 gallons of water. A hose is turned on, and water flows into the pool at the rate of 8 gallons per minute. How many gallons of water will be in the pool after 70 minutes?

Answers

Answer:

40 gallons

Explanation:

the rules is -8x + 600 = y becuase every minute 8 gallons is empty and theres 600 to begin with

x is the number of minutes and y is the numbers of gallons

so you do -8 times 70 plus 600

which will gove you 40

We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of america. According to the preamble which action represents an appropriate role for government

Answers

Answer:

Provide for the common defense

Answer:

Defending the country

Explanation:

The Preamble of the US Constitution spells out the objectives of the new state that was formed: 1- Justice, 2- Internal Tranquility, 3- Common Defense, 4- General Welfare, 5- Freedom. Thus, the Federal State should seek for its mechanisms to achieve these objectives.

Common defense a prominent factor in the preamble of the constitution, the goal through this factor was to defend the country, not only at that time, but over the generations. The preamble makes clear that the defense of the country was one of the main factors that guaranteed the creation of the state and the creation of legislation.

Please help me with this problem?

Answers

Answer:

Explanation:

Let's look at two examples.

y = 4x + 2

y = 4x + 9

These two will never intersect, no matter how long they both are. The reason is because they have a different y intercept (2 and 9).

They are parallel.

Here's the second example

2y = 8x + 16

y = 4x + 8

These are 2 equations that you have been given. If you divide the first one by 2 you get the second one. That means you have an infinite number of solutions. No exceptions.

So the correct answer is C

I think its C not sure tho

SAT No Calculator section question in the picture

Answers

Answer:

Explanation:

I don't think you can really tell. You need one more statement like

BC is equal to AM

Only then will the answer of 1/3 be right.

Answer: 1/3

Explanation:

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