Problem 50462. Calculate quadrilateral Area: sides and diagonals given

Created by mansour torabi

Solve Later

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w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> Round the answer to four decimal places.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Hint: use Bretschneider's 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0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Calculate quadrilateral Area: sides (a,b, c, d) and diagonals (e, f) are given</span></span></div><div style="block-size: 232px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 116px; text-align: left; transform-origin: 384px 116px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">                                                </span></span><img class="imageNode" width="269" height="226" style="vertical-align: baseline;width: 269px;height: 226px" 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" data-image-state="image-loaded"></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style=""></span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style=""> Round the answer to four decimal places.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Hint: use Bretschneider's formula</span></span></div></div></div>

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Rafael S.T. Vieira on 6 Nov 2022

Beautiful formula.

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Problem 50462. Calculate quadrilateral Area: sides and diagonals given

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Problem 50462. Calculate quadrilateral Area: sides and diagonals given

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