The answer will depend on the shape of the triangle and what is known about it.
As written, the statement is false. You can't have it both ways. I suspect you meant to write that dilating a triangle changes the size or area of the triangle but does not change its shape. That would be true.
Doubling the base of a triangle while keeping the height constant will double the area of the triangle. The area of a triangle is directly proportional to its base length, so increasing the base length by a factor of 2 will result in the area being multiplied by 2 as well.
There is only one basic shape for an equilateral triangle. The area can only vary as the length of the sides vary.
Just moving a triangle, or rotating, or even reflecting (without scaling) a shape will not change its area or its perimeter.
#include<iostream> struct shape { virtual double area () const = 0; }; struct triangle : shape { triangle (double b, double h): base (b), height (h) {} double base, height; double area () const override { return base * height / 2; } }; struct circle : shape { circle (double r): radius (r) {} double radius; double area () const override { return 4 * atan(1) * radius * radius; } }; struct rectangle : shape { rectangle (double w, double h): width (w), height (h) {} double width, height; double area () const override { return width * height; } }; int main() { triangle t (10, 5); std::cout << "triangle with base " << t.base << " and height " << t.height << " has area " << t.area() << std::endl; circle c (5); std::cout << "circle with radius " << c.radius << " has area " << c.area() << std::endl; rectangle r (10, 5); std::cout << "rectangle with width " << r.width << " and height " << r.height << " has area " << r.area() << std::endl; }
The area of the triangle would double
area will get 4 times
The answer will depend on the shape of the triangle and what is known about it.
you split your shape in half, (The rectangle and the triangle), by putting a line through it and then calculate the area of the rectangle and then calculate the area of the triangle, half the area of the triangle then add the area of the triangle and the rectangle together!Then you should have your answer!
The shape of the triangle - and its size - will determine its area. There is no information about the triangle provided and so there cannot be a sensible answer.
If the shape is a triangle, then the area is approx 8.2 sq in.
As written, the statement is false. You can't have it both ways. I suspect you meant to write that dilating a triangle changes the size or area of the triangle but does not change its shape. That would be true.
Doubling the base of a triangle while keeping the height constant will double the area of the triangle. The area of a triangle is directly proportional to its base length, so increasing the base length by a factor of 2 will result in the area being multiplied by 2 as well.
least volume and most surface area is 3D triangle
There is only one basic shape for an equilateral triangle. The area can only vary as the length of the sides vary.
Just moving a triangle, or rotating, or even reflecting (without scaling) a shape will not change its area or its perimeter.