Questions tagged [area]

Area is a quantity that expresses the extent of a two-dimensional measurement of a shape.

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Area of a circle passing through two vertices of a parallelogram touching one edge.

For reference: Let $ABCD$ be a parallelogram, $AB = 6, BC= 10$ and $AC = 14$ ; traces a circle passing through the vertices $C$ and $D$ with $AD$ being tangent and this circle is $BC$ a secant. ...
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Find the area inside the curve $r^2=2\cos(5\theta)$ and outside the unit circle.

I found the area of one full rose-petal($A_1$) and the area enclosed by the petal and the unit circle($A_2$), subtracted these from one another to get the area enclosed by the curve outside of the ...
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Area of the region bounded by $f(x)$ and $g(x)$? ($f(x)=|2-x|$ and $g(x)=2-|2-x|$)

$f(x)=|2-x|$ $g(x)=2-|2-x|$ Find the area of the region bounded by $f(x)$ and $g(x)$. I was told that you actually need two definite integrals to solve this problem, since it involved absolute value, ...
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Finding area of a triangle in a quadralateral with only one side known

For a quadrilateral $PQRS$, $PR=40$ and $PS=32$. Suppose for a point $X$ on the line segment $RS$ the triangles $PQX$ and $PRS$ are congruent in that order. If area of triangle $PXS$ is $112$ square ...
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For reference: Calculate the area of ​​the quadrangular region $EBCD$, if $BC = 5$, and $AD = AC$. $P$ is a tangent point. (Answer: $64$) My progress: $\triangle OPD \sim \triangle ADC$ $AD=2OD \... 1answer 90 views Find the area of ​the triangular region$ABC$in the figure bellow For reference: In the figure below, the quadrilaterals$AMNB, AEFC$and$APQR$are squares;$S_1=9\ \mathrm{m^2}$,$S_2(BRE)=6\ \mathrm{m^2}$, calculate the area of ​​the triangular region$ABC$. (... 2answers 52 views Find the area of triangle$RAQ$in the figure below For reference: Through the midpoint$M$of the side$AC$of a triangle$ABC$, a line is drawn that intersects in$BC$in$P$and extended$BA$in$Q$. By$B$, a line parallel to$PQ$is drawn which ... 1answer 69 views $f(x)=3x-\sin(\frac{\pi x}{2})$,$\quadg(x)=x^3+2x-\sin(\frac{\pi x}{2})f:\mathbb R \rightarrow\mathbb R$and$g:\mathbb R \rightarrow\mathbb R$are two functions such that$f(x)=3x-\sin(\frac{\pi x}{2})$,$\quadg(x)=x^3+2x-\sin(\frac{\pi x}{2})$then choose the ... 1answer 44 views Find the area of ​the non-convex pentagonal region AEIDCA. For reference: In triangle$ABC$, the interior angle bisectors$AD$and$CE$are drwan which intersect at$I$. If$\angle B = 60^\circ$and the area of triangular region$AIC$is$A$, calculate the ... 1answer 84 views Find the area of ​the shaded region: in the figure For reference: In the figure, calculate the area of ​​the shaded region if$ML=LN, PM=a, NQ=b, AC=c.$(Answer:$\frac{(a+b)c}{4}$) My progress: Let$ML=LN=BL=x.S_{ALC} = S = S_{APQC}-S_{ALP}-S_{...
Through the centroid $G$ of a triangle $ABC$, a secant line is drawn, cutting sides $AB$ and $BC$. On the straight line a point $E$ is considered. Calculate the area of ​​the triangle $EBG$ if the ...