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Answers
Answer:multiply the length and breadth of the Pentagon
Area= length × breadth.
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Step-by-step explanation:EA
Step-by-step explanation:
Refer the attachment!
Method (1) :
Area of of pentagon = 2 × Area of trapezium
{ As there are two trapeziums; one is ABCF and other one is AEDF. }
= 2(1/2 × Area of trapezium ABCF)
= 2 × 1/2 × Sum of parallel sides × height
= 2/2 × (AF + BC) × CF
Substitute the values,
= (30 + 15) × 15/2
= 45 × 15/2
= 675/2
= 337.5 cm²
Method (2) :
The other way to solve it is, by adding the area of sqaure and triangle. Join line BE; this will divide the pentagon into two shapes (square; below one and triangle; above one). So,
Area of pentagon = Area of sq BCDE + Area of ∆ABE
= (side)² + 1/2 × base × height
= (BC)² + 1/2 × BE × height
Let's say that the point where line BE meets AF is G. So, we can say that height of the triangle ABE is AG. And AG = AF - FG (where FG = CB = DE = 15 cm). So, AG = 30 - 15 = 15 cm. Similarly, BE = CD = 15 cm.
Substitute the values,
= (BC)² + 1/2 × BE × AG
= (15)² + 1/2 × 15 × 15
= 225 + 225/2
= 225 + 112.5
= 337.5 cm²
Method (3) :
Extend point B to X and E to Y such that XY || BE || CD. Due to this we have a rectangular shape. But as we need to find the area of pentagon. So, subtract the area of two side triangles which formed after extending the points from the area of constructed rectangle.
Area of pentagon = Area of rectangle XYDC - 2(Area of ∆XBA)
= length × breath - 2(1/2 × base × height)
= XC × CD - (2/2 × XA × XB)
(XC = AF = 30 cm, CD = 15 cm, XA = XY/2 = 15/2, XB = XC - BC = 30 - 15 = 15 cm)
Substitute the values,
= 30 × 15 - (15/2 × 15)
= 450 - (7.5 × 15)
= 450 - 112.5
= 337.5 cm²
Therefore, the area of pentagon is 337.5 cm².
