Question

Find the missing values:

Answer 1

Hint:The most common findings from such questions are the area of a triangle. The area of the triangle can be simply found by using the formula which is given by
$ Area = \dfrac{1}{2} \times Base \times Height$.Using this formula we try to fill the missing values.

Complete step-by-step answer:
Remember that data given will be in different measurement units. So please make sure that you are dealing with the numbers in the same units for area finding. The area is measured in square units.
Now, we will deal with each part of the question by making different cases which are given below.
(Case1)
\[Given,Base{\text{ }} = {\text{ }}15cm,Area = \;87c{m^2},Height{\text{ }} = ?\] In this case, height is not given, so height needs to find out from the given values of base and area.
$ \Rightarrow Area = \dfrac{1}{2} \times Base \times Height$
$ \Rightarrow 87c{m^2} = \dfrac{1}{2} \times 15cm \times Height$
$ \Rightarrow Height = \dfrac{{87 \times 2}}{{15}} = \dfrac{{58}}{5}$
$\therefore Height = 11.6cm$
(Case2)
\[Given,Height{\text{ }} = 31.4mm,{\text{ }}Area = 1256m{m^2},Base = ?\;\]. In this case, the base is not given, so the base needs to find out from the given values of height and area.
$ \Rightarrow Area = \dfrac{1}{2} \times Base \times Height$
$
   \Rightarrow 1256 = \dfrac{1}{2} \times Base \times 31.4 \\
   \Rightarrow Base = \dfrac{{2 \times 1256}}{{31.4}} \\
 $
$\therefore Base = 80mm$
 (Case 3)
$Given,Base = 22cm,Area = 170.5c{m^2},Height = ?$. In this case, height is not given, so height needs to find out from the given values of base and area.
$
   \Rightarrow Area = \dfrac{1}{2} \times Base \times Height \\
   \Rightarrow Height = \dfrac{{2 \times 170.5}}{{22}} = \dfrac{{170.5}}{{11}} \\
  \therefore Height = 15.5cm \\
 $
The value of missing terms in each of the cases will be summarized below:
Case1) \[Height = {\text{ }}11.6cm\]
Case2) $Base = 80mm$
Case3) $Height = 15.5cm$

Note:In such Questions where we need to find the missing values. Always remember to go for some formulas that will fit with the given data. Once you do that, it will be very easy to find the solution by substituting given values leaving the missing values aside. Students can also make use of formulas derived from trigonometry but such formulas will make this question very lengthy to solve and is not generally needed to solve such an easy question as above.