ABCD is a parallelogram (see figure above). The ratio of DE to EC is $1 : 3$ . Height AE has a length of $3.$ If quadrilateral ABCE has an area of 21,what is the area of ABCD?

Open in App

Solution

First, break quadrilateral ABCE into two pieces: A $3 \times 3 x$ rectangle and a right triangle with a base of $x$ and a height of $3$ .
Therefore, the area of quadrilateral ABCE is given by the following equation:
$(3 \times 3 x) + \frac{3 \times x}{2} = 9 x + 1.5 x = 10.5 x$
If ABCE has an area of 21, then $21 = 10.5 x$ , which reduces to $x = 2$ .

Quadrilateral ABCD is a parallelogram, so we can use the formula:
A = (base) $\times$ (height), or $4 x \times 3$ .
Substitute $x = 2$ , we get
$A = 4 (2) \times 3 = 24$

Suggest Corrections

Similar questions

Q. In the given figure,

∠ A B C = 90^{0} = ∠ D E C, A C = 15 c m

and

A B = 9 c m .

If the area of the quadrilateral

A B C D

72 c m^{2};

find the length of

D E .

Q. ABCD is a quadrilateral, with AB parallel to CD (see figure). Point E is between C and D such that AE represents the height of ABCD, and E is the midpoint of CD. If AB is 4 inches long, AE is 5 inches long, and the area of triangle AED is 12.5 square inches, what is the area of ABCD ? (Note: figure not drawn to scale.)

Q. The area of the parallelogram ABCD is

90 c m^{2}

(see Fig.9.13) EC=FD. Find

A (A B E F)

Question 102

ABCD is a parallelogram in which AE is perpendicular to CD is shown in the given figure. Also, AC = 5 cm, DE = 4 cm and area of $Δ A E D = 6 c m^{2}$ .
Find the perimeter and area of parallelogram ABCD.

A parallelogram ABCD has an area of 150

c m^{2}

. If a diagonal BD is drawn, what is the ratio of the area of

Δ A B D

and the area of

Δ B C D

Join BYJU'S Learning Program

ABCD is a parallelogram (see figure above). The ratio of DE to EC is 1:3. Height AE has a length of 3. If quadrilateral ABCE has an area of 21,what is the area of ABCD?

ABCD is a parallelogram (see figure above). The ratio of DE to EC is $1 : 3$ . Height AE has a length of $3.$ If quadrilateral ABCE has an area of 21,what is the area of ABCD?