Area of Parallelograms

Classroom Resources / Illuminations

Area of Parallelograms

Grade: 6th to 8th

In the diagram below, the blue line is parallel to the base of the parallelogram. When you slide C back and forth along the blue line, how do the base (AB), height (DE), and area change?

Activity

</iframe</div> </div> <div id="ctl00_ctl00_cphMainContainer_cphContent_dzContentArea_uxColumnDisplay_ctl00_uxControlColumn_ctl00_uxWidgetHost_uxWidgetHost_widget_pnlInstructions"> <h3 class="section-header">Instructions</h3> <p> <div id="IN" class="tab_content" style="margin-top:20px;"><h3>How to Use</h3><p> </p><ul><li>Use the red points to adjust the dimensions and location of the parallelogram. </li></ul><p> </p><p><i>Buttons</i></p><ul><li><b>Show/Hide Area</b> will show/hide the area, rounded to the nearest hundredths. </li><li><b>Show/Hide Hint</b> will show/hide the base and height measurements to the nearest thousandths. </li></ul></div> </p> </div> <div id="ctl00_ctl00_cphMainContainer_cphContent_dzContentArea_uxColumnDisplay_ctl00_uxControlColumn_ctl00_uxWidgetHost_uxWidgetHost_widget_pnlExploration"> <h3 class="section-header">Exploration</h3> <p> <div id="EX" class="tab_content" style="margin-top:20px;"><p> </p><p>Before using any of the buttons, explore the following: </p><ul><li>Knowing that the background is a cm. grid, estimate the area of the shown parallelogram. How close were you to the actual? </li><li>What is the relationship between the base, height, and area of the parallelogram? </li><li>Where do you see parallelograms in the real world? When would you need to know its area? </li></ul><p> </p></div> </p> </div> <div id="ctl00_ctl00_cphMainContainer_cphContent_dzContentArea_uxColumnDisplay_ctl00_uxControlColumn_ctl00_uxWidgetHost_uxWidgetHost_widget_pnlObjStd"> <h3 class="section-header">Objectives and Standards</h3> <b>NCTM Standards and Expectations</b><ul><li>Geometry / Measurement</li></ul><ul><li>Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.</li></ul><ul><li>6-8</li></ul><ul><li>Geometry</li></ul> </div> </div>  </div> </div> </div> </li> <li> <div id="ctl00_ctl00_cphMainContainer_cphContent_dzContentArea_uxColumnDisplay_ctl00_uxControlColumn_ctl01_uxWidgetHost_uxUpdatePanel"> <div data-ux-pagebuilder="Widget"> <div class="widgetBody"> <div id="ctl00_ctl00_cphMainContainer_cphContent_dzContentArea_uxColumnDisplay_ctl00_uxControlColumn_ctl01_uxWidgetHost_uxWidgetHost_widget_CB"> <p style="border-top: 3px solid #FFC20E; margin-top: 15px; padding-top: 15px; padding-left: 15px; max-width: 350px;"> <a href="/Classroom-Resources/Illuminations/Adding-Extensions-for-Interactives/" title="Adding Extensions for Interactives">Having Trouble Running the Applet?</a> </p> </div> <span id="ctl00_ctl00_cphMainContainer_cphContent_dzContentArea_uxColumnDisplay_ctl00_uxControlColumn_ctl01_uxWidgetHost_uxWidgetHost_widget_errorLb"></span> </div> </div> </div> </li> <li> <div id="ctl00_ctl00_cphMainContainer_cphContent_dzContentArea_uxColumnDisplay_ctl00_uxControlColumn_ctl02_uxWidgetHost_uxUpdatePanel"> <div data-ux-pagebuilder="Widget"> <div class="widgetBody"> <div class="row adzone-footer"> <div class="col-md-12"> <div class="advertisement">  <div id='div-gpt-ad-1464287580186-1' style='height:90px; width:728px;'> <script type='text/javascript'> googletag.cmd.push(function() { googletag.display('div-gpt-ad-1464287580186-1'); }); </script> </div> </div> </div> </div> </div> </div> </div> </li> </ul> </div> </div> </div> </div> </div> </div> </div> <div class="footer"> <div class="sitemap"> <div class="container"> <div class="row"> <div class="col-md-4"> </div> <div class="col-md-4"> </div> <div class="col-md-4"> </div> </div> </div> </div> <div id="ctl00_ctl00_footer_nctmsocialbar1_pnlMain" class="social"> <div class="container"> <div class="social-links"> <ul> <li><a href="https://twitter.com/nctm" class="twitter" title="Twitter" target="_blank"></a></li> <li><a href="https://www.linkedin.com/company/214550?trk=NUS_CMPY_TWIT" class="linkedin" title="LinkedIn" target="_blank"></a></li> <li><a href="https://instagram.com/nctm.math/" class="instagram" title="Instagram" target="_blank"></a></li> <li><a href="https://www.youtube.com/@NCTMChannel" class="youtube" title="YouTube" target="_blank"></a></li> <li><a href="https://www.facebook.com/TeachersofMathematics" class="facebook" title="Facebook" target="_blank"></a></li>  <li><a href="https://www.tiktok.com/@nctm.math" class="tiktok" title="TikTok" target="_blank"></a></li> </ul> </div> <div class="tweet"> <div class="feed"> </div> </div> </div> </div> <div class="banner"> <div class="container"> <div class="footer-right"> <ul> <li class=''> <a href="http://my.nctm.org">MyNCTM</a> </li> <li class=''> <a href="http://illuminations.nctm.org/">Illuminations</a> </li> <li class=''> <a href="/noticeandwonder/">Notice and Wonder</a> </li> </ul> </div> <div class="footer-left"> <div class="logo"> <a href="#" class="logo-link" title="National Council of Teachers of Mathematics"></a> </div> <div class="address"> 1906 Association Drive <br/> Reston, VA 20191-1502 <br/> (800) 235-7566 or (703) 620-9840 <br/> FAX: (703) 476-2970 <br/> <a href="mailto:nctm@nctm.org" title="nctm@nctm.org">nctm@nctm.org</a> <br/> </div> <div class="address-links"> <ul> <li> <a href='http://mediakits.theygsgroup.com/nctm-2016/audience'>Advertise with NCTM</a> </li> <li> <a href='http://mediakits.theygsgroup.com/nctmevents/home'>Exhibit and Sponsor</a> </li> <li> <a href='/News-and-Calendar/For-the-Media/'>For the Media</a> </li> </ul> </div> </div> <div class="footer-links"> <span class="copyright">Copyright © 2024, National Council of Teachers of Mathematics.</span>  <script> !function(f,e,a,t,h,r){if(!f[h]){r=f[h]=function(){r.invoke? r.invoke.apply(r,arguments):r.queue.push(arguments)}, r.queue=[],r.loaded=1*new Date,r.version="1.0.0", f.FeathrBoomerang=r;var g=e.createElement(a), h=e.getElementsByTagName("head")[0]||e.getElementsByTagName("script")[0].parentNode; g.async=!0,g.src=t,h.appendChild(g)} }(window,document,"script","https://cdn.feathr.co/js/boomerang.min.js","feathr"); feathr("fly", "5d9def21cca930f7d4d95c6e"); feathr("sprinkle", "page_view"); </script> <script type="text/javascript"> _linkedin_partner_id = "5502186"; window._linkedin_data_partner_ids = window._linkedin_data_partner_ids || []; window._linkedin_data_partner_ids.push(_linkedin_partner_id); </script> <script type="text/javascript"> (function(l) { if (!l){window.lintrk = function(a,b){window.lintrk.q.push([a,b])}; window.lintrk.q=[]} var s = document.getElementsByTagName("script")[0]; var b = document.createElement("script"); b.type = "text/javascript";b.async = true; b.src = https://snap.licdn.com/li.lms-analytics/insight.min.js; s.parentNode.insertBefore(b, s);})(window.lintrk); </script> <noscript> <img height="1" width="1" style="display:none;" alt="" src="https://px.ads.linkedin.com/collect/?pid=5502186&fmt=gif" " /> </noscript> <ul> <li> <a href='/Terms/'>Terms of Use</a> </li> <li> <a href='/privacy/'>Privacy Policy</a> </li> <li> <a href='/policies/'>Code of Conduct</a> </li> <li> <a href='/contact-us/'>Contact Us</a> </li> </ul> </div> </div> </div> </div> <script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.0/jquery.min.js"></script> <script src="/assets/js/bootstrap.min.js"></script> <script type="text/javascript" src="/assets/js/jquery.fancybox.pack.js"></script> <script> $(document).ready(function () { $('.fancybox').fancybox({ autoSize: true, padding: 10 }); }); </script> <script src="/assets/js/jquery.stickem.js"></script> <script> $(document).ready(function () { $('.container').stickem(); }); </script> <script src="/assets/js/custom-content-block.js"></script> <script> $(document).ready(function () { // Javascript to enable link to tab var hash = document.location.hash; var prefix = "tab_"; var array = hash.replace(prefix, "").split('-'); if (array.length > 0) { $('.nav-tabs a[href=' + array[0].replace(" ", "") + ']').tab('show'); if (array.length > 1) { location.href = "#" + array[1]; window.location.hash = hash; } } }); </script> <script src="/assets/js/jquery.bootpag.js"></script> <script src="/assets/js/jquery.mobile.custom.min.js"></script> <script> $(document).ready(function() { $("#spotlight-carousel").swiperight(function() { $(this).carousel('prev'); }); $("#spotlight-carousel").swipeleft(function() { $(this).carousel('next'); }); }); </script> <script src="/assets/js/browse-taxonomies.js"></script> <script src="/assets/js/nctm.bookmark.js"></script> <script src="/assets/js/nctm.login.js"></script> <script src="/assets/js/nctm.search.js"></script> <script src="/assets/js/nctm.cart.js"></script> <script src="/assets/js/nctm.twitter.js"></script> <script src="/assets/js/nctm.checkout.js"></script>  <script type="text/javascript"> $('li.pizza').mouseover( function () { $(this).addClass('open') } ); $('li.pizza').mouseout( function () { $(this).removeClass('open') } ); </script>  </div> <span id="ctl00_ctl00_ctlUser"></span> <span id="ctl00_ctl00_ctlShoppingCart"></span> <script type="text/javascript" data-cfasync="false"> (function(W,i,s,e,P,o,p){W['WisePopsObject']=P;W[P]=W[P]||function(){ (W[P].q=W[P].q||[]).push(arguments)},W[P].l=1*new Date();o=i.createElement(s), p=i.getElementsByTagName(s)[0];o.async=1;o.src=e;p.parentNode.insertBefore(o,p) })(window,document,'script','//loader.wisepops.com/get-loader.js?v=1&site=DPtNuFf39i','wisepops'); </script> </form> </body> </html> <script>(function(){if (!document.body) return;var js = "window['__CF$cv$params']={r:'8870d71b3d1b02c0',t:'MTcxNjI1NTQzNi4yOTAwMDA='};_cpo=document.createElement('script');_cpo.nonce='',_cpo.src='/cdn-cgi/challenge-platform/scripts/jsd/main.js',document.getElementsByTagName('head')[0].appendChild(_cpo);";var _0xh = document.createElement('iframe');_0xh.height = 1;_0xh.width = 1;_0xh.style.position = 'absolute';_0xh.style.top = 0;_0xh.style.left = 0;_0xh.style.border = 'none';_0xh.style.visibility = 'hidden';document.body.appendChild(_0xh);function handler() {var _0xi = _0xh.contentDocument || _0xh.contentWindow.document;if (_0xi) {var _0xj = _0xi.createElement('script');_0xj.innerHTML = js;_0xi.getElementsByTagName('head')[0].appendChild(_0xj);}}if (document.readyState !== 'loading') {handler();} else if (window.addEventListener) {document.addEventListener('DOMContentLoaded', handler);} else {var prev = document.onreadystatechange || function () {};document.onreadystatechange = function (e) {prev(e);if (document.readyState !== 'loading') {document.onreadystatechange = prev;handler();}};}})();</script><script src="/cdn-cgi/scripts/7d0fa10a/cloudflare-static/rocket-loader.min.js" data-cf-settings="c0a500d37b6f7d64faafc910-|49" defer></script>

Area of Parallelograms

Activity