Question 8

We will list all parts of the rectangle that we need to measure.

Step 1 — Sides of the Rectangle

We will name the four corners A, B, C, D.

We will measure the length of each side.

The four sides are AB, BC, CD, and DA.

Step 2 — Diagonals of the Rectangle

We will draw two lines connecting opposite corners.

These lines are called diagonals.

The two diagonals are AC and BD.

We will measure the length of each diagonal.

Step 3 — Angles Formed by Diagonals

The two diagonals cross each other at a point.

Let us call this point O.

They form 4 angles at this crossing point.

These angles are $\angle AOB, \angle BOC, \angle COD$, and $\angle DOA$.

Each diagonal makes angles with the sides.

Diagonal AC makes angle $\angle DAC$ with side AD.

It also makes angle $\angle BAC$ with side AB.

Diagonal BD makes angle $\angle ABD$ with side AB.

It also makes angle $\angle CBD$ with side BC.

We will measure these 8 angles.

Step 4 — Other Measurements

We can find the distance around the rectangle.

This is called the perimeter.

We can also find the space inside the rectangle.

This is called the area.

We will measure the perimeter and the area.

Answer

(i) The parameters to track are: The lengths of the four sides (AB, BC, CD, DA). The lengths of the two diagonals (AC, BD). The 8 angles formed by the diagonals: $\angle AOB, \angle BOC, \angle COD, \angle DOA, \angle DAC, \angle BAC, \angle ABD, \angle CBD$. (ii) Other measurements to track are the perimeter and the area of the rectangle.