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

Question

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

Calculate the area of the triangle CEF

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

15 cm²