the diagonal of a quadrilateral is 28 cm in length and the perpendicular to it from the opposite vertices are 6.8cm and8cm respectively find the area of the quadrilateral
To find the area of the quadrilateral, we can divide it into two triangles and then find the sum of their areas.
Let's label the vertices of the quadrilateral as A, B, C, and D, with diagonal BD. And let the perpendiculars from A and C intersect BD at E and F respectively.
First, we need to find the lengths of AE and CF. We are given that AE = 6.8 cm and CF = 8 cm.
Next, we find the lengths of BE and DF. Since the diagonals of a quadrilateral bisect each other, we can see that BE = BD/2 = 28/2 = 14 cm and DF = BD/2 = 28/2 = 14 cm.
Now, to find the area of triangle ABE, we can use the formula for the area of a triangle:
Area of triangle = 1/2 * base * height
In triangle ABE, the base is BE = 14 cm and the height is AE = 6.8 cm. So,
Area of triangle ABE = 1/2 * 14 cm * 6.8 cm = 47.6 cm²
Similarly, the area of triangle CDF can be calculated using the base DF = 14 cm and the height CF = 8 cm:
Area of triangle CDF = 1/2 * 14 cm * 8 cm = 56 cm²
Finally, to find the area of the quadrilateral, we sum the areas of the two triangles:
Area of quadrilateral = Area of triangle ABE + Area of triangle CDF = 47.6 cm² + 56 cm² = 103.6 cm²
Therefore, the area of the quadrilateral is 103.6 cm².
This Question
Very good
clearly, the quadrilateral consists of two triangles, each with a base if 28 cm.
Their altitudes are 6.8 and 8.0 cm.
I'm sure you know how to find the area of a triangle, given its base and height...
Good
the diagonal of a quadrilateral s 28 cm n length and the perpendicular to it from the opposite vertices are 6.8 cm and 8 cm respectively find the area of
(P:.the quadrilateral