Question

Find the area of a parallelogram-shaped shaded region. Also, find the area of each triangle. What is the ratio of the area of shaded portion to the remaining area of the rectangle?

( in attchmnt) -/​

Answer 1

Given:-

• AB = 10cm
• AF = 4cm
• AD = 6cm

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To Find:-

• Area of a parallelogram-shaped shaded region.
• Area of Each Triangle
• Ratio of the area of shaded portion to the remaining area of the rectangle.

Solution:-

Here's we are asked with the Area of Parallelogram-Shaped shaded region . So, we will find the Area of Parallelogram first.

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Here's AB = 10cm

AF = 4cm

FB = 10cm - 4cm = 6cm

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$\begin{gathered} \sf \: Area \: of \: Parallelogram \: = \: Base \: \times \: Height \\ \\ \\ \sf \: Area \: of \: Parallelogram \: =FB \times AD \\\\\\ \: \sf Area\;of\;Parallelogram = 6cm \times 6cm \\ \\ \\ {\pmb{\sf \: Area\;of\;Parallelogram = {36cm}^{2}}} \end{gathered}$

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∴ Hence, The Required area of Shaded region is 36cm²

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$\sf {Area of \triangle DEF = \dfrac{1}{2} \times Base \times Height }$

$\sf {Area = \dfrac{1}{2} \times AF \times AD }$

$\sf {Area = \dfrac{1}{2} \times 4 \times 6 }$

${ \pmb{\sf \: Area \: of \: Rectangle \: = {12cm}^{2} }}$

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Now, To find the Area of Triangle so,

$\begin{gathered} \sf \: Area \: of \: \triangle \: BEC = \dfrac{1}{2} \times Base \times Height \: \\ \\ \\ \sf \: Area \: = \dfrac{1}{2} \times GC \times BC \\ \\ \\ \sf \: Area \: = \dfrac{1}{2} \times \: 4 \times \: 6 \\ \\ \\ { \pmb{\sf \: Area \: = \: {12cm}^{2}}} \end{gathered}$

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$\begin{gathered} \sf \: Area \: of \: Rectangle \: = \: Length \times Breadth \\ \\ \\ \sf \: Area \: of \: Rectangle \: = \sf \: 10cm \: \times 6cm \\ \\ \\ { \pmb{\sf \: Area \: of \: Rectangle \: = {60cm}^{2} }} \end{gathered}$

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$\begin{gathered}\sf Remaining \; Area\; of \; Rectangle \: = {60cm}^{2} - {30cm}^{2} \\ \\ \\ \sf \: Remaining \; Area\; of \; Rectangle \: = {24cm}^{2} \\ \\ \\\sf Required \; Ratio = 36:24 \: \\ \\ \\ = \sf\dfrac { \cancel{36}^{3}}{ \cancel{24_2} } \\ \\ \\ = { \pmb{\sf{\orange {Required \; Ratio \: = 3 \ratio \: 2}}}}\end{gathered}$

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Answer 2

Answer:

cm = 6cm

Step-by-step explanation: