Question

find the area of a field in the shape of a trapezium if one of its dio gonal is 32 m and length of the perpendicular dropped on it from the remaining vertices are 7.5mand 10.5​

Answer 1

Given:

• Measure of the diagonal of the field = 32 m

• Length of the perpendicular dropped on it from the remaining vertices = 7.5 m and 10.5 m.

To calculate:

• Area of the field.

Calculation:

Here, we'll split the quadrilateral into two triangles. The sum of the area of two triangles will be equivalent to the area of the quadrilateral. In both triangles, field's diagonal is base and the height will be the perpendiculars dropped on the diagonal from remaining vertices.

Area of ∆ 1 :

⇒ Area of ∆' = ½ × b × h

⇒ Area of ∆' = ½ × 32 × 7.5 m²

⇒ Area of ∆' = 1 × 16 × $\sf {\cancel{ \dfrac{75}{10} }}$ m²

⇒ Area of ∆' = 1 × 16 × $\sf {\dfrac{15}{2} }$ m²

⇒ Area of ∆' = 1 × 8 × 15 m²

⇒ Area of ∆' = 120 m²

Area of ∆ 2 :

⇒ Area of ∆"= ½ × b × h

⇒ Area of ∆". = ½ × 32 × 10.5 m²

⇒ Area of ∆" = 1 × 16 × $\sf {\cancel{ \dfrac{105}{10} }}$ m²

⇒ Area of ∆" = 1 × 16 × $\sf {\dfrac{21}{2} }$ m²

⇒ Area of ∆" = 1 × 8 × 21 m²

⇒ Area of ∆" = 168 m²

Henceforth,

⇒ Area of the field = Sum of the area of both triangle

⇒ Area of the field = Area of ∆ 1 + Area of ∆ 2

⇒ Area of the field = ( 120 + 168 ) m²

⇒ Area of the field = 288 m²

Therefore, area of the field is 288 m².