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Because the triangle is three sided and a parallelogram is six sided.

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Q: How do you know the area of the triangle is equal to half the area of the parallelogram?

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If the heights and bases are the same, then the triangle is half the area of the parallelogram.

If the heights and bases are the same, then the triangle is half the area of the parallelogram.

you do it because the triangle is half the size of the parallelogram

I don't know about the relation in the perimeters of a triangle and a parallelogram but if a triangle is on the same base on which the parallelogram is and the triangle is between the same parallel lines of the parallelogram, then the area of the triangle will be half the area of the parallelogram. That is, area of a triangle = 1/2 area of a parallelogram if the triangle is on the same base and between the same parallel lines.

Because base times height = the area of a parallelogram and a triangle's area is half that of the parallelogram that the triangle exactly fits into.

Either diagonal of a parallelogram divides the parallelogram into two triangles of equal areas. Thus area of triangle abd = half that of the parallelogram abcd. The required ratio is 1 / 2.

If you put two of ANY triangle hypotenuse to hypotenuse the shape will have 4 sides (thus a parallelogram or quadrilateral).

To get the area it half breadth by height. A simplified thought on this is because the formula for the area of a parallelogram is length by width, and a triangle would be half of this

That would depend on the dimension of the green triage. If the triangle was formed by joining two opposite corners of the parallelogram then it would be half the area of the parallelogram. Area of parallelogram = 15*2 = 30 square cm. 1/2 the area = 15 square cm.

They involve only the base and vertical height.The formula for a triangle is half that for the corresponding parallelogram.

No. Although the area of every triangle is equal to half the area with the same base and height, only right angled triangles are half a rectangle.

If you draw a diagonal in a rectangle you get two equal triangles, each half the area of the rectangle. Area of rectangle is base x height, so half of that is ½ x base x height. QED

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