Question

the figure below,not drawn to scale ,is made up of two identical right angled triangles overlapping each other. find the area of the shaded part ABCD, where AD equals to 3cm.

Answer 1

The area of the shaded portion would be = 5.63cm².

How to calculate the area of the shaded portion?

To calculate the area of the shaded portion, the following steps should be taken as follows:

From the given figure, to area of the shaded portion can be calculated through subtraction of Triangle 1 to Triangle 2.

The area of triangle 1 = ½×base×height.

base = 9cm

height = 5+5+2.5= 12.5

Area = ½× 12.5 × 9

= 6.25×9

= 56.25cm²

The area of triangle 2=

base = 9cm

height = 11.25

Area = ½× 11.25×9

= 101.25/2 = 50.625

The area of the shaded portion;

= 56.25-50.625

= 5.63cm²

Answer 2

We develop two equations based on the given diagram. We let x be the length from C to the point meeting the endpoint of 5. We let y be the length of CD.

First, we determine the length from D to the endpoint of line measuring 9 cm. We use the Pythagorean theorem.
l = sqrt ((3)² + 5²)
l = 5.83

Then, the equations that can be developed or established are:
x² + 6² = y²
9² + (5 + x)² = (y + 5.83)²

In solving for x and y, we use substitution.
From the first equation,
y = sqrt (x² + 36)
We substitute this to the second equation y.

The value of x is 9.51.

y = sqrt (9.51² + 36) = 11.25.

Calculate for the area of the bigger triangle.
A = 0.5(9 cm)(5 + 9.51 cm) = 65.295 cm²

Also calculate for the area of the smaller triangle,
A = (0.5)(6 cm)(9.51 cm) = 28.53 cm²

The difference between the areas is 36.765 cm².

ANSWER: 36.77 cm²