Question

Copy and complete the table for a triangle.

Base	6	5	5	X	16	?	?
Height	10	14	20	2x	?	5	11
Area	?	?	?	?	120	50	110

Answer 1

Hint: For this question we are asked to find the required parameter that is base or area or height of the triangle.
We will solve the given question by using the formulae in areas and perimeters concept which is \[area=\dfrac{1}{2}\times base\times height\] we can find the required
unknown answer by substituting the given values in the formulae.

Complete step by step solution:
In the given first case we are base as 6 and height as 10. We must find the unknown area of the triangle by using the above mentioned formulae.
\[\Rightarrow area=\dfrac{1}{2}\times base\times height\]
\[\Rightarrow area=\dfrac{1}{2}\times 6\times 10\]
\[\Rightarrow area=30unit{{s}^{2}}\]
From the given question in the second case we are given base 8 and height as 14 and asked to find the value of the area of the triangle. So by using the above mentioned formula we can calculate the area as follows.
\[\Rightarrow area=\dfrac{1}{2}\times base\times height\]
\[\Rightarrow area=\dfrac{1}{2}\times 8\times 14\]
\[\Rightarrow area=56unit{{s}^{2}}\]
From the given question in the third case we are given base 5 and height as 20 and asked to find the value of the area of the triangle. So by using the above mentioned formula we can calculate area as follows.
\[\Rightarrow area=\dfrac{1}{2}\times base\times height\]
\[\Rightarrow area=\dfrac{1}{2}\times 5\times 20\]
\[\Rightarrow area=50unit{{s}^{2}}\]
From the given question in the fourth case we are given base x and height as 2x and asked to find the value of the area of the triangle. So by using the above mentioned formula we can calculate area as follows.
\[\Rightarrow area=\dfrac{1}{2}\times base\times height\]
\[\Rightarrow area=\dfrac{1}{2}\times x\times 2x\]
\[\Rightarrow area={{x}^{2}}unit{{s}^{2}}\]
In the given fifth case we are given base as 16 and area as 120. We must find the unknown height by rearranging the above formula of area of triangle and solve for the height as follows.
\[\Rightarrow area=\dfrac{1}{2}\times base\times height\]
Here we get the formula for the height by sending the 2 and base to the left hand side. So the solution of height will be as follows.
\[\Rightarrow height=\dfrac{2\times area}{base}\]
\[\Rightarrow height=\dfrac{2\times 120}{16}\]
\[\Rightarrow height=15units\]
From the given question in the sixth case we are given area 50 and height as 5 and asked to find the value of the base of the triangle. So by using the above mentioned formula after rearrangement we can calculate base as follows. \[\Rightarrow area=\dfrac{1}{2}\times base\times height\]
\[\Rightarrow base=\dfrac{2\times area}{height}\]
\[\Rightarrow base=\dfrac{2\times 50}{5}\]
\[\Rightarrow base=20units\]
From the given question in the seventh case we are given area 110 and height as 11 and asked to find the value of the base of the triangle. So by using the above mentioned formula after rearrangement we can calculate base as follows. \[\Rightarrow area=\dfrac{1}{2}\times base\times height\]
\[\Rightarrow base=\dfrac{2\times area}{height}\]
\[\Rightarrow base=\dfrac{2\times 110}{11}\]
\[\Rightarrow base=20units\]
So the required complete table for the triangle will be as follows.

Base	6	8	5	x	16	20	20
Height	10	14	20	2x	15	5	11
Area	30	56	50	\[{{x}^{2}}\]	120	50	110

Note: Students must be very careful while performing the calculations and students must be having knowledge in areas and perimeters of 2D figures. Students must not do mistakes like using a wrong formula of triangle for example if we use \[\Rightarrow area=base\times height\] for first case the solution will be\[\Rightarrow area=6\times 10\]\[\Rightarrow area=60\] which is wrong for a triangle.