【数学】 Ratio of Triangle Area りんぺん比 解説用の図

SAT sample Q1

Suppose you are given the following two triangles.

One angle is shared and therefore identical.

Answer.

Let us make the shared angle "θ".

Then, the area of red triangle is 「2 x 4 x sinθ」.

The area of blue triangle is 「8 x 6 x sinθ」.

Therefore, without knowing any other information, we know the ratio of the red to the blue triangle is 2x4/8x6 = 1/6

Generalization

SAT sample Q2

What is the ratio of the wing in the following butterfly.

Answer

Generalization

The area ratio of left wing to right wing is a x A : b x B.

One step beyond

If you have 2 triangles with one of these angles is supplemental to each other.

Then the area ratio is

AxB : axb

.

SAT example Q3

Answer.