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# help with geometry

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Let line AC be perpendicular to line CE. Connect A to the mid-point of CE which is D, and connect E to the mid-point of AC which is B.  If AD and EB intersect at point F, BC=CD=15cm, then find the area of △DFE.

Jul 24, 2020

#1
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Let line AC be perpendicular to line CE. Connect A to the mid-point of CE which is D, and connect E to the mid-point of AC which is B.  If AD and EB intersect at point F, BC=CD=15cm, then find the area of △DFE.

Hello Guest!

$$\overline{BE}=\sqrt{(15^2+30^2)cm^2}=\sqrt{1125cm^2}=33.541cm\\ \overline{EF}=\frac{1}{2}\cdot \overline{BE}$$

$$\large \frac{h_{△DFE}}{15cm}=\frac{\frac{1}{2}\cdot \overline{BE} }{\overline{BE}}=\frac{1}{2}$$

$$h_{△DFE}=7.5cm$$

$$A_{△DFE}=\frac{1}{2}\cdot \overline{ED}\cdot h_{△DFE}=\frac{1}{2}\cdot 15cm\cdot 7.5cm$$

$$A_{△DFE}=56.25cm^2$$ !

Jul 24, 2020
edited by asinus  Jul 24, 2020
edited by asinus  Jul 24, 2020
#3
+1

You have an error here:::

EF ≠ 1/2 * BE                    EF = 2/3 * BE

The centroid divides a median into two line segments, and their ratio is 2 : 1

Dragan  Jul 24, 2020
#2
+1

Let line AC be perpendicular to line CE. Connect A to the mid-point of CE which is D, and connect E to the mid-point of AC which is B.  If AD and EB intersect at point F, BC=CD=15cm, then find the area of △DFE.

AD = BE = sqrt( 302 + 152 )

FE = 2/3BE

Now we have all 3 sides of a triangle DFE.

We can use Heron's formula to calculate the area of this triangle.

Area of  △DFE = 75 cm

Jul 24, 2020
edited by Dragan  Jul 24, 2020