(Continued from above)Properties and important points to remember-
• Opposite sides are parallel and congruent (). E.g.
AB & DC, and AD & BC.
• The diagonals bisect each other i.e. the point of intersection of the diagonals, divides each diagonal into two equal parts.
• The two diagonals are congruent ().
• A square is a special case of a rectangle where all the four sides are of the same length.
• It can also be said to be a special case of a parallelogram, but that the angles are 90°.
• Each diagonal divides the rectangle into two congruent right triangles and each of the triangles have the same area, which equals to half the area of the rectangle.
• If the length, width and height of the triangle is represented by (l, w,
h),
the area of a rectangle is given by the formula: A = (w*h).
Each diagonal equals to: (w2 +
h2)
Example 3: Given- the rectangle as shown in the figure below. Find out the area.
Notice that diagonal = 13, and one side equals to 5 units.
Such problems requires you to find an additional piece of information, to enable you work
out the area. Here you may use the Pythagorean Theorem to find the base of the rectangle
before finding the area i.e.
c2 = a2 + b2 132 = 52 + b2.
When simplified, it gives
b = 12
Area of rectangle =
b * h
=
12 * 5 = 60 (units)2, as the final answer.
Example 4: Given- in the diagram below (NTS), ABCD is a rectangle with
AE = EF = FB. What is the ratio of the area of the triangle CEF and that of the rectangle?
Step 1: Let, CB = b and AB = 3a AE = EF = FB = a(given)
Step 2: Area of rectangle ABCD = 3a * b = 3ab
Step 3: Area of triangle CEF = 1/2(a)(b) = (1/2)ab
Therefore, ratio of the area of the triangle CEF and that of the rectangle
ABCD is
= (1/2)ab / 3ab
=1/6, as thr final answer.
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). E.g.
AB & DC, and AD & BC.
(w2 +
h2)
