The length of a diagonal of a
quadrilateral-shaped field is 48 m and the
lengths of perpendiculars dropped on it
from the opposite vertices are 16 m and
26 m. Find the area of the field.
Answers
Answer: 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;
Area of quadrilateral
= Area of Triangle ABC + Area of Triangle ADC
Area of Triangle =(1/2) ×Height ×Base
In Triangle ABC
Base (AC) =24 m, height (h1) =13 m
Area of Triangle ABC =(1/2) ×13×24= 156 m²
Area of Triangle ABC =156 m²
In Triangle ADC
Base (AC) =24 m, height (h2) =8 m
Area of Triangle ADC
=(1/2) ×8×24= 96 m²
Area of Triangle ADC =96 m²
Area of the field = Area of Triangle ABC + Area of Triangle ADC
=156 + 96 = 252 m²
Area of the field = 252 m²
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Hope this will help you...
Step-by-step explanation:
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