How does the area of the triangle relate to the area of the square? Please Explain!!! I really don't get it!

1 answer:

4 0

A square has 4 right angles and 4 equal sides.
If you draw a diagonal through the square then you get two right triangles. So the area relation between a square and a right triangle is going to be half. The area of the triangle is half the area of the square.

Also the formula for area of a square is length times width.
And the formula for the area of a right triangle is 0.5 times length times width.

So if you set up the equation (let's use * as multiplication symbol ):

Area of a Square : Area of a Right Triangle
length * width : 0.5 * length * width
(Divide by length * width on both sides)
1:0.5 or 2:1

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Points M, N, and P are respectively the midpoints of sides AC , BC , and AB of △ABC. Prove that the area of △MNP is on fourth of

Hunter-Best [27]

Answer:

The area of △MNP is one fourth of the area of △ABC.

Step-by-step explanation:

It is given that the points M, N, and P are the midpoints of sides AC, BC and AB respectively. It means AC, BC and AB are median of the triangle ABC.

Median divides the area of a triangle in two equal parts.

Since the points M, N, and P are the midpoints of sides AC, BC and AB respectively, therefore MN, NP and MP are midsegments of the triangle.

Midsegments are the line segment which are connecting the midpoints of tro sides and parallel to third side. According to midpoint theorem the length of midsegment is half of length of third side.

Since MN, NP and MP are midsegments of the triangle, therefore the length of these sides are half of AB, AC and BC respectively. In triangle ABC and MNP corresponding side are proportional.

$\triangle ABC \sim \triangle NMP$