Question

Which of the following has a greater area ?
A parallelogram with one side 24 cm and the distance between parallel sides 9cm or a quadrilateral having one diagonal 24cm and the perpendiculars to the diagonal are 9cm and 12cm

Answer 1

Answer:

parallelogram

Step-by-step explanation:

parallelogram has more area then quadrilateral

Answer 2

★ Procedure :

Here, we are given two quadrilaterals :

• a) A parallelogram
• b) An irregular quadrilateral

In order to find which one have greater area, we have to calculate the area of both shapes. To calculate the area of parallelogram, we'll use the formula : Base × height. To calculate the area of the irregular quadrilateral, we'll divide into two triangles and will find by adding the area of both triangles.

After that, we'll compare which one has greater area.

Solution:

~ Area of parallelogram :

Given:

• Measure of one side (say base) = 24 cm

• Distance between parallel sides (Height) = 9 cm

Therefore,

→ Area of ||gm = Base × Height

→ Area of ||gm = 24 cm × 9 cm

→ Area of ||gm = 216 cm ²

~ Area of quadrilateral having one diagonal 24cm and the perpendiculars to the diagonal are 9cm and 12cm :

Let us draw a rough diagram first (Refer to the attachment : Fig B). Clearly, ABD & CBD are two triangles. Henceforth,

→ Area of quadrilateral = Area of ( ∆ ABD & ∆ CBD ) cm²

→ Area of quadrilateral = (½ × b × h) + (½ × b × h) cm²

→ Area of quadrilateral = (½ × 9 × 24) + (½ × 12 × 24) cm²

→ Area of quadrilateral = (1 × 9 × 12) + ( 1 × 6 × 24 ) cm²

→ Area of quadrilateral = ( 108+144 ) cm²

→ Area of quadrilateral = 252 cm²

Therefore, area of quadrilateral having one diagonal 24cm and the perpendiculars to the diagonal are 9cm and 12cm has greater area. $\checkmark$