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.

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.