Which two figures out of the following four have the same area (with same units) ?
\n(Figure 1: Right triangle with sides 14, 22, 90 degree angle)
\n(Figure 2: Square with side 12)
\n(Figure 3: Isosceles triangle with sides 22, 22, 22)
\n(Figure 4: Circle with radius 7)<\/p>\n
[amp_mcq option1=”1 and 3″ option2=”1 and 2″ option3=”2 and 4″ option4=”1 and 4″ correct=”option4″]<\/p>\n
Figure 2: Square with side 12.
\nArea\u2082 = side\u00b2 = 12\u00b2 = 144 sq units.<\/p>\n
Figure 3: Isosceles triangle with sides 22, 22, 22. This is an equilateral triangle with side length 22.
\nArea\u2083 = (\u221a3 \/ 4) * side\u00b2 = (\u221a3 \/ 4) * 22\u00b2 = (\u221a3 \/ 4) * 484 = 121\u221a3 sq units.
\nUsing \u221a3 \u2248 1.732, Area\u2083 \u2248 121 * 1.732 \u2248 209.5 sq units.<\/p>\n
Figure 4: Circle with radius 7.
\nArea\u2084 = \u03c0 * radius\u00b2 = \u03c0 * 7\u00b2 = 49\u03c0 sq units.
\nUsing the approximation \u03c0 \u2248 22\/7 (often used in problems involving multiples of 7):
\nArea\u2084 \u2248 49 * (22\/7) = 7 * 22 = 154 sq units.<\/p>\n
Comparing the areas:
\nArea\u2081 = 154
\nArea\u2082 = 144
\nArea\u2083 \u2248 209.5
\nArea\u2084 \u2248 154 (using \u03c0 \u2248 22\/7) or \u2248 153.9 (using \u03c0 \u2248 3.14)<\/p>\n