An equilateral triangle with a base of 20 cm and a height of 17.3 cm is divided into 4 smaller equilateral triangles. What is true about this figure? A. The total perimeter of all 4 triangles is 70 cm. B. The total area of all 4 small triangles is the same as the area of the big triangle, 173 cm2. C. The total perimeter of all 4 triangles is 90 cm. D. The total area of one of the small triangles is 173 cm2.
area scale ratio is 1/4 so every length of a small one is 1/2 the big one's length
the perimeter of the big one is 60
so the perimeter of each small one is 30 and the total is 120, not 70
SO A is FALSE
B is true 10*17.3
C FALSE as shown above
D false obviously 173/4 in fact
To solve this question, we need to find the perimeter and area of one of the small triangles and then determine the total perimeter and total area of all four small triangles.
To find the perimeter of one of the small triangles, we note that the equilateral triangle has all three sides equal. Since the base of the big triangle is 20 cm, each side of the big triangle is also 20 cm.
Now, we can use the height of the big triangle (17.3 cm) to find the height of one of the small triangles. The height of the small triangle is the same as the height of the big triangle, so each small triangle has a height of 17.3 cm.
We can use the height and the formula for the perimeter of an equilateral triangle to find the perimeter of one of the small triangles. The formula for the perimeter of an equilateral triangle is P = 3s, where P is the perimeter and s is the length of each side. In this case, since the height is the same as the side length, the perimeter of one of the small triangles is 3 * 17.3 cm = 51.9 cm.
Next, to find the area of one of the small triangles, we can use the formula for the area of an equilateral triangle. The formula for the area of an equilateral triangle is A = (s^2 * √3) / 4, where A is the area and s is the length of each side. In this case, since the side length is 17.3 cm, the area of one of the small triangles is (17.3^2 * √3) / 4 ≈ 125.29 cm^2.
Now, we can determine the total perimeter and total area of all four small triangles. Since there are four small triangles, the total perimeter is 4 * 51.9 cm = 207.6 cm. Similarly, the total area is 4 * 125.29 cm^2 = 501.16 cm^2.
Based on these calculations, we can conclude that the correct answer is:
B. The total area of all 4 small triangles is the same as the area of the big triangle, 173 cm^2.