","comment":{"@type":"Comment","text":" Since the equation of the area of the triangle is $\\dfrac{1}{2}\\times \\text{base}\\times \\text{height}$, then find the height and base from the figure and substitute them into the formula."},"encodingFormat":"text/markdown","suggestedAnswer":[{"@type":"Answer","encodingFormat":"text/html","text":" $$10$$","position":0},{"@type":"Answer","encodingFormat":"text/html","text":" $$40$$","position":2},{"@type":"Answer","encodingFormat":"text/html","text":" none of the above","position":3}],"acceptedAnswer":[{"@type":"Answer","encodingFormat":"text/html","text":" $$20$$","position":1,"answerExplanation":{"@type":"Comment","text":" $$\\text{From the figure: } \\\\ \\text{Base } = 8 \\\\ \\text{Height } = 5 \\\\ \\text{Area of } \\vartriangle \\text{ ABC =}\\dfrac{1}{2}\\times 8\\times 5=20 $$ ","encodingFormat":"text/html"},"comment":{"@type":"Comment"}}]},{"@type":"Question","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","educationalLevel":"beginner","name":"Area using geometry Quiz 1","text":" Find the area of shaded figure: $$ \\\\ $$","comment":{"@type":"Comment","text":" Divide the figure into three triangles EDC,ABC,EAF respectively and then apply the area of the triangle to calculate the individual area and then obtain its sum."},"encodingFormat":"text/markdown","suggestedAnswer":[{"@type":"Answer","encodingFormat":"text/html","text":" $$12$$","position":0},{"@type":"Answer","encodingFormat":"text/html","text":" $$24$$","position":1},{"@type":"Answer","encodingFormat":"text/html","text":" $$48$$","position":3}],"acceptedAnswer":[{"@type":"Answer","encodingFormat":"text/html","text":" $$32$$","position":2,"answerExplanation":{"@type":"Comment","text":" $$\\text{Area of the figure: } \\\\ \\text{Area }={{\\text{A}}_{1}}+{{\\text{A}}_{2}}+{{\\text{A}}_{3}} \\\\ \\Rightarrow \\Delta EDC+\\Delta AFE+\\Delta ABC \\\\ \\Rightarrow \\dfrac{1}{2}\\times 16\\times (6-4)+\\dfrac{1}{2}\\times (-8)\\times (-4)+\\dfrac{1}{2}\\times 8\\times 4 \\\\ \\Rightarrow 32+16-16 \\\\ \\Rightarrow 32 $$ ","encodingFormat":"text/html"},"comment":{"@type":"Comment"}}]},{"@type":"Question","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","educationalLevel":"beginner","name":"Area using geometry Quiz 1","text":" Find the area of shaded region in the figure: $$ \\\\ $$
","comment":{"@type":"Comment","text":" First divide the figure such that there is one triangle and three trapezium and then apply the formula of area of triangle $\\dfrac{1}{2}\\times \\text{base}\\times \\text{height}$ and area of trapezium $\\dfrac{1}{2}\\times \\text{distance between parallel sides}\\times (\\text{Sum of the parallel sides)}$."},"encodingFormat":"text/markdown","suggestedAnswer":[{"@type":"Answer","encodingFormat":"text/html","text":" $$7$$","position":0},{"@type":"Answer","encodingFormat":"text/html","text":" $$14$$ ","position":1},{"@type":"Answer","encodingFormat":"text/html","text":" $$56$$","position":3}],"acceptedAnswer":[{"@type":"Answer","encodingFormat":"text/html","text":" $$28$$ ","position":2,"answerExplanation":{"@type":"Comment","text":" $$\\text{Area of the figure = } \\\\ \\Delta ABC + $$ Trapezium $$(AGHI) + $$ Trapezium $$(AGCF) + $$ Trapezium $$(EFCD) \\\\ \\Rightarrow \\dfrac{1}{2}\\times 8\\times (6-3)+\\dfrac{1}{2}\\times (3+2)\\times 2+\\dfrac{1}{2}\\times (8+4)(3-2)+\\dfrac{1}{2}\\times (3+2)\\times (8-6) \\\\ \\Rightarrow 12+5+6+5 \\\\ \\Rightarrow 28$$","encodingFormat":"text/html"},"comment":{"@type":"Comment"}}]},{"@type":"Question","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","educationalLevel":"beginner","name":"Area using geometry Quiz 1","text":" Find the area: $$ \\\\ $$
","comment":{"@type":"Comment","text":" Divide the figure into parts such that there are two triangles AFE,BCD and one trapezium ABDF and then use the formula of their area and find its sum."},"encodingFormat":"text/markdown","suggestedAnswer":[{"@type":"Answer","encodingFormat":"text/html","text":" $$7$$","position":0},{"@type":"Answer","encodingFormat":"text/html","text":" $$14$$ ","position":1},{"@type":"Answer","encodingFormat":"text/html","text":" $$56$$","position":3}],"acceptedAnswer":[{"@type":"Answer","encodingFormat":"text/html","text":" $$24.5$$ ","position":2,"answerExplanation":{"@type":"Comment","text":" $$\\text{Area of figure= } \\\\ \\Delta AFE + \\Delta BCD + \\text{ Trapezium } ABDE \\\\ \\Rightarrow \\dfrac{1}{2}\\times 4\\times 2+\\dfrac{1}{2}\\times 3\\times 2+\\dfrac{1}{2}\\times (3+4)\\times 5 \\\\ \\Rightarrow 4+3+17.5 \\\\ \\Rightarrow 24.5 $$ ","encodingFormat":"text/html"},"comment":{"@type":"Comment"}}]},{"@type":"Question","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","educationalLevel":"beginner","name":"Area using geometry Quiz 1","text":" Find the perimeter: $$ \\\\ $$
","comment":{"@type":"Comment","text":" In the figure use Pythagoras theorem and since ${{H}^{2}}={{B}^{2}}+{{P}^{2}}$ therefore we get the length of slat side as $\\sqrt{2}$."},"encodingFormat":"text/markdown","suggestedAnswer":[{"@type":"Answer","encodingFormat":"text/html","text":" $$11+\\sqrt{2}$$","position":0},{"@type":"Answer","encodingFormat":"text/html","text":" $$12+2\\sqrt{2}$$","position":1},{"@type":"Answer","encodingFormat":"text/html","text":" $$13+3\\sqrt{2}$$","position":2}],"acceptedAnswer":[{"@type":"Answer","encodingFormat":"text/html","text":" $$14+4\\sqrt{2}$$","position":3,"answerExplanation":{"@type":"Comment","text":" $$\\text{There are a total of 14 edges with length of 1 unit} \\\\ \\text{In the given figure and 4 edges with length }\\sqrt{2} \\text{unit} \\\\ \\text{Then the required perimeter }=14+4\\sqrt{2}$$","encodingFormat":"text/html"},"comment":{"@type":"Comment"}}]}]}