In the diagram below, $BE=EC=DF,$ and $\triangle ADF$ has the same area as $\triangle DEF.$ If rectangle $DXYF$ has area $42,$ what is the area of $\triangle ABC$? [asy] size(0,4cm); pair B=(-3,0); pair C=(5,0); pair A=(2,3); pair D=(A+B)/2; pair E=(B+C)/2; pair F=(C+A)/2; pair W=(-0.5,3); pair X=(-0.5,0); pair Y=(3.5,0); pair Z=(3.5,3); draw(A--B--C--cycle); draw(D--E--F--cycle); dot(A); dot(B); dot(C); dot(D); dot(E); dot(F); dot(X); dot(Y); //dot(W); dot(Z); label("$A$",A,N); label("$B$",B,SW); label("$C$",C,SE); label("$D$",D,NW); label("$E$",E,S); label("$F$",F,NE); draw(D--X,dashed); draw(F--Y,dashed); label("$X$",X,S); label("$Y$",Y,S); //label("$W$",W,N); //label("$Z$",Z,N); draw(X+(0.25,0)--X+(0.25,0.25)--X+(0,0.25)); draw(Y-(0.25,0)--Y+(-0.25,0.25)--Y+(0,0.25)); //draw(W+(0.25,0)--W+(0.25,-0.25)--W+(0,-0.25)); //draw(Z+(-0.25,0)--Z+(-0.25,-0.25)--Z+(0,-0.25)); [/asy]

Question

11-06-2022
Mathematics

contestada

In the diagram below, $BE=EC=DF,$ and $\triangle ADF$ has the same area as $\triangle DEF.$ If rectangle $DXYF$ has area $42,$ what is the area of $\triangle ABC$? [asy] size(0,4cm); pair B=(-3,0); pair C=(5,0); pair A=(2,3); pair D=(A+B)/2; pair E=(B+C)/2; pair F=(C+A)/2; pair W=(-0.5,3); pair X=(-0.5,0); pair Y=(3.5,0); pair Z=(3.5,3); draw(A--B--C--cycle); draw(D--E--F--cycle); dot(A); dot(B); dot(C); dot(D); dot(E); dot(F); dot(X); dot(Y); //dot(W); dot(Z); label("$A$",A,N); label("$B$",B,SW); label("$C$",C,SE); label("$D$",D,NW); label("$E$",E,S); label("$F$",F,NE); draw(D--X,dashed); draw(F--Y,dashed); label("$X$",X,S); label("$Y$",Y,S); //label("$W$",W,N); //label("$Z$",Z,N); draw(X+(0.25,0)--X+(0.25,0.25)--X+(0,0.25)); draw(Y-(0.25,0)--Y+(-0.25,0.25)--Y+(0,0.25)); //draw(W+(0.25,0)--W+(0.25,-0.25)--W+(0,-0.25)); //draw(Z+(-0.25,0)--Z+(-0.25,-0.25)--Z+(0,-0.25)); [/asy]

Respuesta :

Otras preguntas

Question 7 Which is the quotient of 1/5 divided by 3??

I need helpppp The main function of the immune system is to provide _______ to the body, which is defined as the body’s ability to protect itself from pathogen

In your opinion, what are the 2 best methods of distributing the one cookie amongst 25 people?What are the advantages and disadvantages for each of your methods

the bottom of the inner curve of a hook is called

Use the distributive property to rewrite 4(c - 9)

Analyzing an Element of a Greek Myth Achilles's fatal flaw is a problem for him because he is a warrior. he is a king he is invincible. he is a god.

In the top row labeled Before Collision, two train cars approach one another with a grey arrow pointing to each car. The left car has below it m subscript 1 = 6

How to say I love you Kristen Stewart

You are hiking in a forest and come upon a mysterious plant, which you determine is either a lycophyte sporophyte or a pterophyte sporophyte. Which of the follo

I NEED HELP!! Choose either adjectives or pronouns and use the space provided to do the following: Explain what language would be like without the existence of

Lanuel Lanuel · Answer 1 · 2022-06-14T03:06:07+02:00

Based on the calculations, the area of triangle ABC is equal to 84 units².

How to calculate the area of a triangle?

Mathematically, the area of a triangle can be calculated by using this formula:

Area = 1/2 × b × h

Where:

b is the base area.

h is the height.

By critically observing the diagram (see attachment), we can logically deduce that ΔABC can be divided into four (4) congruent triangles i.e ΔADF, ΔBDE, ΔDEF, and ΔEFC. Also, ΔDEF is half the area of rectangle DXYF.

Thus, the area of ΔABC is given by:

ΔABC = 42/2 × 4

ΔABC = 21 × 4

ΔABC = 84 units².

Read more on area of triangle here: brainly.com/question/21917592

#SPJ1

Complete Question:

In the diagram below, BE = EC = DF, and ΔADF has the same area as ΔDEF. If rectangle DXYF has area 42 what is the area of ΔABC?