Question

Find the missing values:

Base	Height	Area of triangle
15 cm	-	87 \(cm^2\)
-	31.4 mm	1256 \(mm^2\)
22 cm	-	170.5 \(cm^2\)

Answer 1

\(\text{Area of a triangle}=\frac{1}{2}\times\text{Base}\times\text{Height}\)
(a) \(b = 15 \;cm\)
\(h=?\)

\(Area = \frac{1}{2}\times b\times h=87\; cm^2\)

\(\frac{1}{2}\times15\times h=87\;cm^2\)

\(h= \frac{87\times2}{15}=11.6\;cm^2\)

Therefore, the height of such triangle is \(11.6\) \(cm\).

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(b) \(b = ?\)
\(h=31.4\; mm\)

\(Area=\frac{1}{2}\times b\times h=1256 \; mm^2\)

\(b = \frac{1256\times2}{31.4}=80\; mm\)

Therefore, the base of such triangle is \(80 \) \(mm\).

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(c) \(b = 22 \;cm ,\;h = ?\)

\(Area=\frac{1}{2}\times b\times h=170.5\; cm^2\)

\(\frac{1}{2}\times 22\times h=170.5\;cm^2\)

\(h=\frac{170.5\times2}{22}=15.5\;cm\)

Therefore, the height of such triangle is \(15.5\) \(cm\).