In △abc point d is the midpoint of ab , point e is the midpoint of bc , and point f is the midpoint of be . find area of △abc, if area of △dcf= 63 cm.

The area of the triangle ABC is 168 cm square.

Explanation:

Let the area of the triangle ABC be x cm square.

It is given that In △ABC point D is the midpoint of  AB , point E is the midpoint of  BC , and point F is the midpoint of  BE .

As we know that a median of a triangle divides the area of a triangle in two equal parts. Since D is a midpoint of AB and AD is median of triangle ABC. So area of triangle ACD and BCD is half of the area of triangle ABC.

The area of ACD and BCD is .

Since E is a midpoint of BC and DE is median of triangle BCD. So area of triangle BDE and CDE is half of the area of triangle BCD.

The area of BDE and CDE is .

Since F is a midpoint of BE and DF is median of triangle BDE. So area of triangle BDF and DEF is half of the area of triangle BDE.

The area of BDF and DEF is . As shown in below figure.

It is given that the area of △DCF= 63 cm.

From the figure the area of △DCF is,

Therefore the area of triangle ABC is 168 cm square.

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

answer is (b.

164 ft2)

a base  

18

b base  

7

h height  

8