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Geometry math help tangram?
https://www.google.com/search?q=tangram&client=ms-... the triangle at the top the area is 4 how do i find the lengths of all the sides
1 Answer
- ?Lv 75 years ago
The top triangle and the left-hand triangle are congruent, isosceles right triangles.
The area of any triangle is ½bh (½ base × height). Here, the base and height are the same: the sides that meet at the center of the outer square. Since the area is 4, we have 4 = ½bh = ½b² (since b = h); therefore b² = 8, and b (and h) = 2√2. The two hypotenuses each have length √((2√2)² + (2√2)²) = √16 = 4.
The small triangles at the upper right and just below the center are isosceles right triangles (and congruent) also. Their legs are ½ the length of those of the large triangles: √2. Their hypotenuses are ½ the length of the side of the outer square: 2.
The smaller square, to the right of center, has sides that are ½ the length of the legs of the large triangles: √2.
The medium-size right triangle at lower right has legs equal to ½ the side of the outer square (2), so its hypotenuse is √8, or 2√2.
The longer sides of the parallelogram equal the hypotenuse of the middle triangle: 2. The shorter sides equal ½ the length of the lower-right triangle's hypotenuse: √2.
