Final answer:
A quadrilateral is a four-sided shape and a rhombus is a quadrilateral with equal-length sides; however, only a square has both equal-length sides and right angles. Vectors can form right angle triangles with their components, and you can use the Pythagorean theorem to find their resultant vector. The area of a circle within a square is approximately three-quarters of the square's area.
Step-by-step explanation:
The statement that a quadrilateral is a four-sided shape is true. A rhombus is indeed a type of quadrilateral, and it is characterized by having four sides of equal length. However, the question's claim that a rhombus is also known as a square is partially misleading. While both a rhombus and a square have sides of equal length, the distinguishing feature of a square is that all of its angles are right angles (each measuring 90 degrees), which is not a requirement for a rhombus. Therefore, all squares are rhombuses, but not all rhombuses are squares.
When it comes to vectors and their components, it is also true that a vector can form the shape of a right angle triangle with its x and y components. This is because the x and y components of a vector act as the legs of the triangle, and the vector itself serves as the hypotenuse. Utilizing the Pythagorean theorem, we can calculate the length of the resultant vector when the components are at right angles to each other.
With regards to area calculation, considering a circle within a square, the circle's area is indeed smaller than that of the square. If the square has a side length 'a', then the area of the square is a², and the area of the circle with radius 'r' can be approximated to be around three-quarters of the square's area, which correlates with the general formula for the area of a circle, πr². Thus, understanding the relationship between geometric shapes can greatly aid in the comprehension of these concepts.
The quadrangle or 'quad' is a term related to topographic maps published by the United States Geological Survey and is defined by longitude and latitude lines. Although this is an important distinction in geography, it is not directly related to the geometric properties of quadrilaterals discussed above.