Category : 7th Class
Mensuration
Standard Units of Area
The inter relationship among various units of measurement of area are listed below.
\[1\,{{m}^{2}}\] = \[(100\times 100)\,c{{m}^{2}}={{10}^{4}}\,c{{m}^{2}}\]
\[1\,{{m}^{2}}\] = \[(10\times 10)\,d{{m}^{2}}=100\,d{{m}^{2}}\]
\[1\,d{{m}^{2}}\] = \[(10\times 10)\,c{{m}^{2}}=100\,c{{m}^{2}}\]
\[1\,da{{m}^{2}}\] = \[(10\times 10)\,{{m}^{2}}=100\,{{m}^{2}}\]
\[1\,h{{m}^{2}}\] = \[(100\times 100)\,{{m}^{2}}={{10}^{4}}{{m}^{2}}\]
\[1\,k{{m}^{2}}\] = \[(1000\times 1000)\,{{m}^{2}}={{10}^{6}}\,{{m}^{2}}\]
\[1\,hectare\] = \[10000\,{{m}^{2}}\]
\[1\,k{{m}^{2}}\] = \[100\,hectare\]
Formula Related to Perimetre and Area
Example:
Find the area of a right-angled triangle whose sides are 15 cm, 9 cm and 2 cm.
(a) \[48\,c{{m}^{2}}\] (b) \[80\,c{{m}^{2}}\]
(c)\[54\,c{{m}^{2}}\] (d) \[78\,c{{m}^{2}}\]
(e) None of these
Answer (c)
Explanation: Here, a = 15 cm, b = 9 cm and c = 12 cm
Also, \[{{a}^{2}}={{b}^{2}}+{{c}^{2}}\Rightarrow \]The given triangle is a right triangle.
\[\therefore \]Area of the right triangle \[=\frac{1}{2}\times 9\times 12=54\,c{{m}^{2}}\]
Example:
The dimensions of the floor of a room are 15 m and 20 m. How many square tiles each of length 20 cm are required to furnish the floor?
(a) 2,400 (b) 5,200
(c) 7,500 (d) 5,250
(e) None of these
Answer (c)
Explanation: Area of the room \[=15\,m\times 20\,m\]
\[=1500\,cm\times 2000\,cm=3\times {{10}^{6}}\,c{{m}^{2}}\]
Area of a tile \[=20\,cm\times 20\,cm=400\,c{{m}^{2}}\]
Total number of tiles required \[=\frac{3\times {{10}^{6}}}{400}=\frac{30000}{4}=7,500\]
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