Answer:
[tex]1008\text{ m}^2[/tex]
Step by step explanation:
Please find the attachment.
We have been given that the length of a diagonal of a quadrilateral shaped field Is 48 m. The length of perpendicular dropped on it from the remaining apposite vertices are 16 m and 26 m.
We can see from our attachment that diagonal AC divides our quadrilateral field into two triangular fields and AC will be the base of both triangles.
To find the area of our given quadrilateral we will find the areas of both triangles and add the areas.
Let us find area of triangle ABC with base 48 m and height 26 m.
[tex]\text{Area of triangle}=\frac{1}{2}(\text{ Base}\times\text{ Height})[/tex]
[tex]\text{Area of triangle ABC}=\frac{1}{2}\times 48\times 26[/tex]
[tex]\text{Area of triangle ABC}=24\times 26[/tex]
[tex]\text{Area of triangle ABC}=624[/tex]
Therefore, the area of triangle ABC will be 624 square meters.
Now let us find area of triangle ADC with base 48 m and height 16 m.
[tex]\text{Area of triangle ADC}=\frac{1}{2}\times 48\times 16[/tex]
[tex]\text{Area of triangle ADC}=24\times 16[/tex]
[tex]\text{Area of triangle ADC}=384[/tex]
Therefore, the area of triangle ADC will be 384 square meters.
Now let us add areas of triangles ABC and ADC to get the area of our quadrilateral ABCD.
[tex]\text{Area of quadrilateral ABCD}=384+624[/tex]
[tex]\text{Area of quadrilateral ABCD}=1008[/tex]
Therefore, the area of quadrilateral shaped field will be 1008 square meters.
