The hexagon PQRSTU is plotted on a coordinate plane with vertices P(–1, 0), Q(–1, 3), R(1, 4), S(2, 5), T(4, 4), and U(4, 0). What is the hexagon's area?
21 sq. units
12 sq. units
24 sq. units
18 sq. units
Answers
Answer: Area of hexagon = 21 sq. unit
Step-by-step explanation:
Area of rectangle abgf = 3*5= 15
Area of rectangle chge= 1*3=3
Area of triangle bch=1/2 * 2 * 1= 1
Area of triangle die= 1/2 * 2 * 1=1
Area of triangle dci= 1/2 * 1 * 1 = 1/2
Total area = 15+3+1+1+(1/2)= 20.5= 21 sq. units
Answer: The area of hexagon PQRSTU is 21 sq. units.
Step-by-step explanation:
When we plot points P,Q,R,S,T,U on the pane it gives us a hexagon depicted in the figure. To find out the area of the given hexagon, we divide it into two rectangles and two triangles.
We will get our answer by adding all these areas.
- Area of rectangle PQAU:
Note: Point A is assumed by us, for ease in calculation.
Area = base x height
= PU x PQ
= 5 x 3
= 15 sq. units.
- Area of rectangle BRTA:
Note: Point A is assumed by us, for ease in calculation.
Area = base x height
= 3 x 1
= 3 sq. units.
- Area of triangle QRB:
Area = 1/2 x base x height
= 1/2 x 2 x 1
= 1 sq. units.
- Area of triangle RST:
Area = 1/2 x base x height
= 1/2 x 4 x 1
= 2 sq. units.
Area of PQRSTU = Area of PQAU + Area of BRTA + Area of QRB + Area of RST.
Required area = 15 + 3 + 1 + 2
= 21 sq. units.
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