OlympiadEasyGeometry7–9

In triangle $ABC$ , $D$ is the midpoint of $BC$ and $E$ is the midpoint of $AD$ . The area of $ABC$ is $48$ cm². What is the area of triangle $BEC$ , in cm²?

No triângulo $ABC$ , $D$ é o ponto médio de $BC$ e $E$ é o ponto médio de $AD$ . A área de $ABC$ é $48$ cm². Qual é a área do triângulo $BEC$ , em cm²?

Answer options

Solution

Step 1 of 3

1.Triangles $ABC$ and $BEC$ share the base $BC$ , so their areas are in the ratio of the distances from $A$ and from $E$ to the line $BC$ .

In triangle ABCABCABC, DDD is the midpoint of BCBCBC and EEE is the midpoint of ADADAD. The area of ABCABCABC is 484848 cm². What is the area of triangle BECBECBEC, in cm²?

Answer options

In triangle $ABC$ , $D$ is the midpoint of $BC$ and $E$ is the midpoint of $AD$ . The area of $ABC$ is $48$ cm². What is the area of triangle $BEC$ , in cm²?