Question

Find a function that models the area A of a square in terms of the diagonal d.

Answer 1

@Directrix

Answer 2

From Geometry, recall that the area of a rhombus can be found by the formula:

Area = (1/2)*d1*d2, where d1 and d2 are the lengths of the two diagonals.

Answer 3

A square is a type of rhombus so that formula applies to the square.

Answer 4

Also, recall from Geometry that the diagonals of a square are congruent.

So, in the area formula:

Area = (1/2)*d1*d2, where d1 and d2, d1 = d2.

Answer 5

Let the diagonal of the square in question just be d.

Area = (1/2) d * d = ? @ninab731

Answer 6

So then would then our answer be just 1/2d^2

Answer 7

Yes. Write that as an equation: A = (1/2) d^2.

Answer 8

Cool thanks :) so now about function that models the diagonal d of a square in terms of the perimeter

Answer 9

I know that perimeter of a square is all the sides

Answer 10

@Directrix one more ? Please :)

Answer 11

From Geometry, recall that the diagonal of a square has measure √2 * a side of a square. This is a result of applying the Pythagorean theorem.

So, d = √2 * a side of a square