Question

"Question 4 The diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. Find the area of the field.

Class 8 Mensuration Page 178"

Answer 1

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...

Answer 2

Hlo mahira this is the answer