Can You Find the Shaded Area? | #math | #geometry

Comments · 14

• ロプ

  @ロプノールs · 6 days ago

  考え方（how to solve) &nbsp;yellowの△を直角二等辺三角形＆①：②：√３の△に分けて考える。<br>高さ（h)を求める。斜辺４から高さ＝２√２......①。<br>底辺（b)を求める。①：√３＝２√２：？　？＝２√６　２√２+２√６.....②<br>yellowの△の面積（area)=①×②×１/２。２√２×（２√２+２√６）×１/２＝（８+８√３）/２＝４+４√３（４で括る）<br>＝４（１+√３）。　answer=4(1+√3)

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• MR

  @MrPaulc222 · 6 days ago

  Height is 2*sqrt(2) (from 4/sqrt(2) on the left triangle).<br>Therefore, PQS area is 4.<br>As PSR is a 30 60 90, SR = 2*sqrt(6)<br>2*sqrt(2)*sqrt(6) = 2*sqrt(12) = 4*sqrt(3) for the right side.<br>Total are 4 + 4*sqrt(3) = approx 10.93 un^2

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• GR

  @gregoryzlotnik5071 · 6 days ago

  Легкая задача, решил за 5 минут.

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• LI

  @libbychang413 · 6 days ago

  |PS| = |QS| = 4*√2/2 = 2*√2<br>|PS| = |PR|*sin(30°) = |PR|/2 -&gt; |PR| = 4*√2<br>|SR| = |PR|*cos(30°) =|PR|*√3/2 =2*√2*√3<br>|QR| = 2*√2*(1+√3)<br>area(△PQR) = |QR|*|PS|/2 = 2*√2*(1+√3)*2*√2/2 = 4*(1+√3)

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• OL

  @ollitrop46 · 6 days ago

  PQS: 4²=x²+x²==16=2x²==8=x²==2√2=x. so 30º-60º-90º PRS sides are 2√2, 2√6, 4√2 Area of PQS: <br>A=½×2√2×2√2==A=√2×2√2==A=4units²==== Area of PRS: A=½×2√2×2√6==A=√2×2√6==A=4√3units²<br>Area of PQR: A=4+4√3==A=4(1+√3)units²

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• BK

  @bkarazi · 5 days ago

  Hello,<br>Yes, it is very easy to find.<br>According to the laws of physics, in the figure shown; <br>a) &nbsp;The base = 2 * sides ➣ 4 = √‾(2 * √₂̅)² + (2 * √₂̅)² u ➣<br> &nbsp; &nbsp; ➣ PS = PQ = 2 * √₂̅ &nbsp;u ➣ PR = 2 * (2 * √₂̅)= 4 * √₂̅ u.<br>b) &nbsp;SR = √‾(4 * √₂̅ )² - (2 * √₂̅)² = 2 * √‾₆ u.<br> &nbsp; &nbsp; Two ways to find the total area:<br>1) &nbsp;Use QR as the base for one large triangle.<br>2) &nbsp;Add the left-side triangle and the right-side triangle areas.<br>a₁) &nbsp;QPS area = (2 * √₂̅) * (2 * √₂̅) ÷ 2 = &nbsp;(4 sq u).<br>b₂) &nbsp;RSP area = (2 * √‾₆) * (2 * √₂̅) ÷ 2 = (4 * √₃ sq u).<br>c) &nbsp; Total area = (4 sq u) + (4 * √₃ sq u) = 4 + (4 * &nbsp;√₃) sq u ≈ 10.928 sq u.<br>Total area = 10.928 sq u.<br>It should not take more than 40 seconds to solve the question. &nbsp;Especially, knowing: “a) The base = 2 * sides” <br>Thank you,

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