Question

Check the picture...​

Answer 1

Answer:

(ɪ) ᴀʀᴇᴀ ᴏꜰ ᴛʀɪᴀɴɢʟᴇ :- 1/2×ʙ×ʜ

1/2×15×ʜ=87

ʜ=87×2/15

ʜ=11.6ᴄᴍ

(ɪɪ)ᴀʀᴇᴀ ᴏꜰ ᴛʀɪᴀɴɢʟᴇ :- 1/2×ʙ×ʜ

1/2×ʙ×31.4=1256

ʙ=1256×31.4/2

ʙ= 80ᴍᴍ

(ɪɪɪ)ᴀʀᴇᴀ ᴏꜰ ᴛʀɪᴀɴɢʟᴇ :- 1/2×ʙ×ʜ

1/2×22×ʜ=170.5

ʜ=170.5×22/2

ʜ=15.5ᴄᴍ

Answer 2

Answer:

Question :

Find the missing values.

$\begin{gathered}\begin{gathered}\begin{gathered} \footnotesize\boxed{\begin{array}{c|c|c}\bf Base &\bf Height & \bf Area({Triangle)}\\\frac{\qquad\qquad}{}&\frac{\qquad\qquad\qquad}{}&\frac{\qquad \qquad \qquad\qquad \qquad}{}\\\sf 15 \: cm &\sf \rule{35pt}{0.1pt} & \sf 87 \: {cm}^{2} \\ \\ \sf \rule{30pt}{0.1pt} & \sf 31.4\:mm & \sf 1256 \: {mm}^{2} \\ \\ \sf 22 \: cm & \sf \rule{35pt}{0.1pt} & \sf 1705\:{cm}^{2} \\ \end{array}}\end{gathered}\end{gathered}\end{gathered}$

$\begin{gathered}\end{gathered}$

Solution :

1) Base - 15cm, Area of Triangle - 87 cm²

• ✧ Base of triangle = 15 cm
• ✧ Area of triangle = 87 cm²
• ✧ Height of triangle = ?

Finding the height of triangle by using area of triangle formula :

${\longrightarrow{\pmb{\sf{Area_{(Triangle)} = \dfrac{1}{2} \times Base \times Height}}}}$

Substituting all the given values in the formula to find height of triangle :

$\begin{gathered} \qquad{\longrightarrow{\sf{Area_{(Triangle)} = \dfrac{1}{2} \times Base \times Height}}}\\\\\qquad{\longrightarrow{\sf{87 \: {cm}^{2} = \dfrac{1}{2} \times 15 \times Height}}}\\\\\qquad{\longrightarrow{\sf{87 \: {cm}^{2} = \dfrac{1 \times 15}{2} \times Height}}}\\\\\qquad{\longrightarrow{\sf{87 \: {cm}^{2} = \dfrac{15}{2} \times Height}}}\\\\\qquad{\longrightarrow{\sf{Height = 87 \times \dfrac{2}{15}}}}\\\\\qquad{\longrightarrow{\sf{Height = \frac{87 \times 2}{15}}}}\\\\\qquad{\longrightarrow{\sf{Height = \frac{174}{15}}}}\\\\ \qquad{\longrightarrow{\sf{Height = \cancel{\frac{174}{15}}}}}\\\\\qquad{\longrightarrow{\sf{\underline{\underline{\pink{Height = 11.6 \: cm}}}}}}\\ \end{gathered}$

Hence, the height of triangle is 11.6 cm.

$\qquad$━━━━━━━━━━━━

2) Height - 31.4 mm, Area of Triangle - 1256 mm².

• ✧ Height of triangle = 31.4 mm
• ✧ Area of triangle = 1256 mm².
• ✧ Base of triangle = ?

Finding the base of triangle by using area of triangle formula :

${\longrightarrow{\pmb{\sf{Area_{(Triangle)} = \dfrac{1}{2} \times Base \times Height}}}}$

Substituting all the given values in the formula to find base of triangle :

$\begin{gathered} \qquad{\longrightarrow{\sf{Area_{(Triangle)} = \dfrac{1}{2} \times Base \times Height}}}\\\\ \qquad{\longrightarrow{\sf{1256 \: {mm}^{2} = \dfrac{1}{2} \times Base \times 31.4}}}\\\\\qquad{\longrightarrow{\sf{1256 \: {mm}^{2} = \dfrac{1 \times 31.4}{2} \times Base}}} \\ \\ \qquad{\longrightarrow{\sf{1256 \: {mm}^{2} = \dfrac{31.4}{2} \times Base}}} \\ \\ \qquad{\longrightarrow{\sf{1256 \: {mm}^{2} = \cancel{\dfrac{31.4}{2}} \times Base}}} \\ \\ \qquad{\longrightarrow{\sf{1256 \: {mm}^{2} = 15.7\times Base}}} \\ \\ \qquad{\longrightarrow{\sf{Base = \frac{1256}{15.7}}}}\\\\\qquad{\longrightarrow{\sf{Base = \cancel{\frac{1256}{15.7}}}}} \\ \\ \qquad{\longrightarrow{\sf{\underline {\underline{\pink{Base = 80 \: mm}}}}}} \end{gathered}$

Hence, the base of triangle is 80 mm.

$\qquad$━━━━━━━━━━━━

3) Base - 22 cm, Area of Triangle - 170.5 cm².

• ✧ Base of triangle = 22 cm
• ✧ Area of triangle = 170.5 cm²
• ✧ Height of triangle = ?

Finding the height of triangle by using area of triangle formula :

${\longrightarrow{\pmb{\sf{Area_{(Triangle)} = \dfrac{1}{2} \times Base \times Height}}}}$

Substituting all the given values in the formula to find height of triangle :

$\begin{gathered} \qquad{\longrightarrow{\sf{Area_{(Triangle)} = \dfrac{1}{2} \times Base \times Height}}}\\\\ \qquad{\longrightarrow{\sf{170.5 \: {cm}^{2} = \dfrac{1}{2} \times 22 \times Height}}}\\\\\qquad{\longrightarrow{\sf{170.5 \: {cm}^{2} = \dfrac{1 \times 22}{2} \times Height}}} \\ \\ \qquad{\longrightarrow{\sf{170.5 \: {cm}^{2} = \dfrac{22}{2} \times Height}}} \\ \\ \qquad{\longrightarrow{\sf{170.5 \: {cm}^{2} = \cancel{\dfrac{22}{2}} \times Height}}} \\ \\ \qquad{\longrightarrow{\sf{170.5 \: {cm}^{2} = 11\times Height}}} \\ \\ \qquad{\longrightarrow{\sf{Height = \frac{170.5}{11}}}}\\\\\qquad{\longrightarrow{\sf{Height = \cancel{\frac{170.5}{11}}}}} \\ \\ \qquad{\longrightarrow{\sf{\underline {\underline{\pink{Height = 15.5 \: cm}}}}}} \end{gathered}$

Hence, the height of triangle is 15.5 cm.

$\begin{gathered}\end{gathered}$

Final Answer :

$\begin{gathered}\begin{gathered}\begin{gathered} \footnotesize\boxed{\begin{array}{c|c|c}\bf Base &\bf Height & \bf Area({Triangle)}\\\frac{\qquad\qquad}{}&\frac{\qquad\qquad\qquad}{}&\frac{\qquad \qquad \qquad\qquad \qquad}{}\\\sf 15 \: cm &\sf 11.6 \: cm & \sf 87 \: {cm}^{2} \\ \\ \sf 80 \: mm & \sf 31.4\:mm & \sf 1256 \: {mm}^{2} \\ \\ \sf 22 \: cm & \sf 15.5 \: cm & \sf 1705\:{cm}^{2} \\ \end{array}}\end{gathered}\end{gathered}\end{gathered}$

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