"Question 11 Diagram of the adjacent picture frame has outer dimensions = 24 cm × 28 cm and inner dimensions 16 cm × 20 cm. Find the area of each section of the frame, if the width of each section is same.
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:
In Figure (I) and (II) are similar in dimensions & also figures (III) and (IV) are similar in dimensions.
Width is 28- 24= 4 cm
Width is same of each section.
Width is height of all the trapezium.
Area of figure (I) = Area of trapezium
= ½(sum of parallel sides) ( height)
= ½ (28+20)(4)
= ½( 48)(4)
= 48×2
= 96 cm²
Area of figure (II) = 96 cm²
Area of figure (I) = Area of figure (II) = 96 cm²
Area of figure (III)
= Area of trapezium = ½(sum of parallel sides) ( height)
= ½(24+16)(4)
= ½(40)(4)
= 40× 2
= 80 cm²
Area of figure (IV) = 80 cm²
Area of figure (III) = Area of figure (IV) = 80 cm²
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Hope this will help you...
