Deltoid Geometry: Calculate Triangle CEF Area with 1:3 Ratio and 20 cm² Reference

Given the deltoid ABCD

and the deltoid AFCE whose area is 20 cm².

The ratio between AO and OC is 1:3

the angle ADC⦠. is equal to the angle ACD⦠.

AD is equal to 8

888DDDCCCAAABBBOOOFFFEEE

Calculate the area of the triangle CEF

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Step-by-step video solution

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00:00 Calculate the area of triangle CEF
00:03 Chapter Title
00:12 Equal diagonals in a parallelogram
00:18 Ratio of sides according to given data
00:33 The entire side (AC) equals the sum of its parts (CO+AO)
00:42 Let's substitute appropriate side values in ratio and solve for OC
00:45 Multiply numerator and denominator by 2 to find common denominator
00:56 This is the length of OC
01:05 Now let's calculate the area of triangle CEF
01:13 (height(OC) multiplied by side(FE)) divided by 2
01:17 Let's substitute appropriate values and solve for the area
01:25 And this is the solution to the question

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1

Understand the problem

Given the deltoid ABCD

and the deltoid AFCE whose area is 20 cm².

The ratio between AO and OC is 1:3

the angle ADC⦠. is equal to the angle ACD⦠.

AD is equal to 8

888DDDCCCAAABBBOOOFFFEEE

Calculate the area of the triangle CEF

3

Final Answer

15 cm²

Practice Quiz

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Indicate the correct answer

The next quadrilateral is:

AAABBBCCCDDD

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