Abcd is a parallelogram ae is perpendicular to dc

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. See Answer See Answer See Answer done loading Question:In the diagram, ABCD is a parallelogram. Point E is on DC with AE perpendicular to DC, and point F is on CB with AF perpen(licular to CB. If AE 20, AF-32, and cos(ZEAF) what is the area of quadrilateral AECF? 32 20 508 V3 448 388 (B) B 568 V3 328 (E) 20 V3 V3 V3

ABCD is a parallelogram in which AE is perpendicular to CD (Fig. 9.54). Also AC = 5 cm, DE = 4 cm, and the area of ∆ AED = 6 cm². Find the perimeter and area of ABCD. Solution: It is given that Area of ∆ AED = 6 cm² AC = 5 cm DE = 4 cm We know that Area of triangle = 1/2 × base × height Area of triangle AED = 1/2 × DE × AE Substituting the values 6 = 1/2 × 4 × AE By further calculation AE = (6 × 2)/4 AE = 3 cm In right angled triangle AEC AE = 3 cm AC = 5 cm Using the Pythagoras theorem EC² = AC² - AE² Substituting the values EC² = 5² - 3² EC² = 25 - 9 EC² = 16 So we get EC = 4 cm DE + EC = DC DC = 4 + 4 = 8 cm Here ABCD is a parallelogram AB = DC = 8 cm In right angled triangle AED Using Pythagoras theorem AD² = AE² + ED² Substituting the values AD² = 3² + 4² AD² = 9 + 16 AD² = 25 So we get AD = 5 cm AD = BC = 5 cm Here ABCD is a parallelogram We know that Perimeter of parallelogram ABCD = 2 (l + b) = 2 (DC + AD) Substituting the values = 2 (8 + 5) = 2 (13) = 26 cm Similarly Area of parallelogram ABCD = base × height = DC × AE Substituting the values = 8 × 3 = 24 cm² Therefore, the perimeter of ABCD is 26 cm and the area is 24 cm². ✦ Try This: The perimeter of a rhombus is 30 cm and one diagonal is 3 cm long then the length of the other diagonal is ☛ Also Check: NCERT Exemplar Class 7 Maths Chapter 9 Problem 102 ABCD is a parallelogram in which AE is perpendicular to CD (Fig. 9.54). Also AC = 5 cm, DE = 4 cm, and the area of ∆ AED = 6 cm². Find the perimeter and area of A...

In parallelogram ABCD, CD = AB= 16 cm [Opposite sides of a parallelogram are equal] We know that, Area of a parallelogram = Base × Corresponding altitude Area of parallelogram A B C D = C D × A E = A D × C F 16 c m × 8 c m = A D × 10 c m A D = 16 × 8 10 c m = 12.8 c m Thus, the length of AD is 12.8 cm.

Hint: First, we must need to know about the parallelogram. Which is the quadrilateral with the two pairs of parallel sides in the geometry. The facing sides and opposite sides of the parallelogram are the lengths in equal and opposite angles in the given parallelogram are equally measured. It is more like the square in shape, but not exactly because in the square all the sides are equal but not in the parallelogram. Formula used: Area of the parallelogram is $A = b \times h$, where b is the breadth and h is the height. Complete step by step answer: From the given information we construct a diagram of the parallelogram using AE is perpendicular to DC and CF is perpendicular to AD. First, we need to find the area of the given parallelogram by the first side and then we will find the second side too. After that, by comparing both of these sides we will find the value of AD. Since from the information and diagram we see that $AE \bot DC,CF \bot AD$ and $AB = 16cm$, $AE = 8cm$and $CF = 10cm$ We need to find the value of AD, So, $AB = DC = 16cm$(opposite sides of the given parallelogram are equal) First find the area of the parallelogram, with the height AE and the base DC. The area of the parallelogram ABCD is $ = b \times h$ The area of the parallelogram ABCD is $DC \times AE = 16 \times 8$ Thus, we get the area of the parallelogram as $128c$ Now to find the area of the parallelogram for the CF as height and AD as the base. Thus, we get the area of the parallelogram as $ABCD =...