benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / The vertices of a convex pentagon are (−1,−1),(−3,4),(1,7),(6,5) and (3,−1). What is the area of the pentagon? [asy] import graph; size(150); real lsf=0.5; pen dps=linewidth(0.7)+f…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

The vertices of a convex pentagon are (−1,−1),(−3,4),(1,7),(6,5)(-1, -1), (-3, 4), (1, 7), (6, 5) and (3,−1)(3, -1). What is the area of the pentagon? [asy] import graph; size(150); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-4.5,xmax=7.5,ymin=-2.5,ymax=8.5; pen zzzzzz=rgb(0.6,0.6,0.6); /*grid*/ pen gs=linewidth(0.7)+zzzzzz; real gx=1,gy=1; for(real i=ceil(xmin/gx)*gx;i<=floor(xmax/gx)*gx;i+=gx) draw((i,ymin)--(i,ymax),gs); for(real i=ceil(ymin/gy)*gy;i<=floor(ymax/gy)*gy;i+=gy) draw((xmin,i)--(xmax,i),gs); Label laxis; laxis.p=fontsize(10); string blank(real x){return "";} xaxis(xmin,xmax,defaultpen+zzzzzz+linewidth(1.2),above=true); yaxis(ymin,ymax,defaultpen+zzzzzz+linewidth(1.2),above=true); draw((-1,-1)--(3,-1)); draw((3,-1)--(6,5)); draw((1,7)--(6,5)); draw((-1,-1)--(-3,4)); draw((-3,4)--(1,7)); dot((-1,-1),ds); dot((-3,4),ds); dot((6,5),ds); dot((3,-1),ds); dot((1,7),ds); clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); [/asy]
Plain-text mathematical notation (without MathML)
The vertices of a convex pentagon are (−1,−1),(−3,4),(1,7),(6,5) and (3,−1). What is the area of the pentagon? [asy]
import graph; size(150); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-4.5,xmax=7.5,ymin=-2.5,ymax=8.5;

pen zzzzzz=rgb(0.6,0.6,0.6);

/*grid*/ pen gs=linewidth(0.7)+zzzzzz; real gx=1,gy=1;
for(real i=ceil(xmin/gx)*gx;i<=floor(xmax/gx)*gx;i+=gx) draw((i,ymin)--(i,ymax),gs); for(real i=ceil(ymin/gy)*gy;i<=floor(ymax/gy)*gy;i+=gy) draw((xmin,i)--(xmax,i),gs);

Label laxis; laxis.p=fontsize(10); string blank(real x){return "";}

xaxis(xmin,xmax,defaultpen+zzzzzz+linewidth(1.2),above=true); yaxis(ymin,ymax,defaultpen+zzzzzz+linewidth(1.2),above=true); draw((-1,-1)--(3,-1)); draw((3,-1)--(6,5)); draw((1,7)--(6,5)); draw((-1,-1)--(-3,4)); draw((-3,4)--(1,7));

dot((-1,-1),ds); dot((-3,4),ds); dot((6,5),ds); dot((3,-1),ds); dot((1,7),ds);

clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);

[/asy]
Original LaTeX notation
The vertices of a convex pentagon are $(-1, -1), (-3, 4), (1, 7), (6, 5)$ and $(3, -1)$. What is the area of the pentagon? [asy]
import graph; size(150); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-4.5,xmax=7.5,ymin=-2.5,ymax=8.5;

pen zzzzzz=rgb(0.6,0.6,0.6);

/*grid*/ pen gs=linewidth(0.7)+zzzzzz; real gx=1,gy=1;
for(real i=ceil(xmin/gx)*gx;i<=floor(xmax/gx)*gx;i+=gx) draw((i,ymin)--(i,ymax),gs); for(real i=ceil(ymin/gy)*gy;i<=floor(ymax/gy)*gy;i+=gy) draw((xmin,i)--(xmax,i),gs);

Label laxis; laxis.p=fontsize(10); string blank(real x){return "";}

xaxis(xmin,xmax,defaultpen+zzzzzz+linewidth(1.2),above=true); yaxis(ymin,ymax,defaultpen+zzzzzz+linewidth(1.2),above=true); draw((-1,-1)--(3,-1)); draw((3,-1)--(6,5)); draw((1,7)--(6,5)); draw((-1,-1)--(-3,4)); draw((-3,4)--(1,7));

dot((-1,-1),ds); dot((-3,4),ds); dot((6,5),ds); dot((3,-1),ds); dot((1,7),ds);

clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle);

[/asy]

level

Level 4

type

Geometry

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
88ce129d-b430-57f5-af8b-0034b53bbd9e
task_key
geometry--test--88ce129d-b430-57f5-af8b-0034b53bbd9e
task_revision_id
1
config / split
geometry / test

Official source

initial import