"Question 10 There is a pentagonal shaped park as shown in the figure. For finding its area Jyoti and Kavita divided it in two different ways. Find the area of this park using both ways. Can you suggest some other way of finding its area?
Class 8 Mensuration Page 178"
Answers
Mensuration:
Mensuration is the branch of mathematics which concerns itself with the measurement of Lengths, areas & volume of different geometrical shapes or figures.
Plane Figure: A figure which lies in a plane is called a plane figure.
For e.g: a rectangle, square, a rhombus, a parallelogram, a trapezium.
Perimeter:
The perimeter of a closed plane figure is the total length of its boundary.
In case of a triangle or a polygon the perimeter is the sum of the length of its sides.
Unit of perimeter is a centimetre (cm), metre(m) kilometre(km) e.t.c
Area: The area of the plane figure is the measure of the surface enclose by its boundary.
The area of a triangle are a polygon is the measure of the surface enclosed by its sides.
A square centimetre (cm²) is generally taken at the standard unit of an area. We use square metre (m²) also for the units of area.
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Solution;
By Jyoti’s diagram:
Area of Trapezium= ½ × (Sum of parallel sides) × Perpendicular distance
Area of pentagon = Area of trapezium ABCP + Area of trapezium AEDP
= ½ (AP + BC) x CP + ½ (ED + AP) x DP
=½ (30 + 15 ) x CP + ½ (15 + 30) xDP
= ½ (30 + 15) (CP + DP)
= ½ X 45 x CD [CP + DP = CD]
= ½ x 45 x 15 =337.5 m²
Area of pentagon =337.5 m²
By Kavita’s diagram
A perpendicular is drawn from the vertex of a triangle to the base of a triangle. height of a triangle = 30 - 15 = 15 m & base =15 m
Area of Triangle= ½ x base x height
Area of square = side x side
Area of pentagon
= Area of triangle ABE + Area of square BCDE
=½ x15 x 15+(15 x15) = ½ x 225 + 225
= 112.5 + 225.0
= 337.5 m²
Hence total area of pentagon shaped park = 337.5 m²
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Hope this will help you...
Mensuration:
Mensuration is the branch of mathematics which concerns itself with the measurement of Lengths, areas & volume of different geometrical shapes or figures.
Plane Figure: A figure which lies in a plane is called a plane figure.
For e.g: a rectangle, square, a rhombus, a parallelogram, a trapezium.
Perimeter:
The perimeter of a closed plane figure is the total length of its boundary.
In case of a triangle or a polygon the perimeter is the sum of the length of its sides.
Unit of perimeter is a centimetre (cm), metre(m) kilometre(km) e.t.c
Area: The area of the plane figure is the measure of the surface enclose by its boundary.
The area of a triangle are a polygon is the measure of the surface enclosed by its sides.
A square centimetre (cm²) is generally taken at the standard unit of an area. We use square metre (m²) also for the units of area.
==========================================================
Solution;
By Jyoti’s diagram:
Area of Trapezium= ½ × (Sum of parallel sides) × Perpendicular distance
Area of pentagon = Area of trapezium ABCP + Area of trapezium AEDP
= ½ (AP + BC) x CP + ½ (ED + AP) x DP
=½ (30 + 15 ) x CP + ½ (15 + 30) xDP
= ½ (30 + 15) (CP + DP)
= ½ X 45 x CD [CP + DP = CD]
= ½ x 45 x 15 =337.5 m²
Area of pentagon =337.5 m²
By Kavita’s diagram
A perpendicular is drawn from the vertex of a triangle to the base of a triangle. height of a triangle = 30 - 15 = 15 m & base =15 m
Area of Triangle= ½ x base x height
Area of square = side x side
Area of pentagon
= Area of triangle ABE + Area of square BCDE
=½ x15 x 15+(15 x15) = ½ x 225 + 225
= 112.5 + 225.0
= 337.5 m²
Hence total area of pentagon shaped park = 337.5 m²
=========================================================
Hope this will help you...