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# In the diagram below, and has the same area as If rectangle has area 42 what is the area of ? ​]

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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 $$\triangle ABC$$? ]

Jan 29, 2021

### Best Answer

#1
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Notice that ABC can be divided into 4 congruent triangles (specifically triangles ADF, BDE, DEF, and EFC). We just need to find the area of one of these triangles and multiply by 4.

Also notice that DEF is half the area of DXYF. Therefore, the area of ABC is equal to $$\frac{42}{2} \cdot 4 = \boxed{84}$$

Jan 29, 2021

### 2+0 Answers

#1
+1
Best Answer

Notice that ABC can be divided into 4 congruent triangles (specifically triangles ADF, BDE, DEF, and EFC). We just need to find the area of one of these triangles and multiply by 4.

Also notice that DEF is half the area of DXYF. Therefore, the area of ABC is equal to $$\frac{42}{2} \cdot 4 = \boxed{84}$$

textot Jan 29, 2021
#2
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Very nice, textot !!!!   CPhill  Jan 29, 2021