Calculate the Area of a Modified Rectangle: 6cm × 7cm with Erased Segment

Question

The shape below consists of a rectangle from which the line segment BH has been erased.

AB = 6 cm

AH = 7 cm

EF = 3 cm

HG = 12 cm

BC = 3 cm

Calculate the area of the shape shaded orange.

Video Solution

Solution Steps

00:19 Let's find the area of the brown shape.

00:22 First, we calculate the area of triangle A B C.

00:26 Multiply height 7, by base 6, then divide by 2.

00:31 That's the area of triangle A B C.

00:35 Now, use the same formula to find the area of triangle H G D.

00:42 This gives us the area of triangle H G D.

00:49 Next, complete B H into a square.

00:56 Calculate its area as side 3, squared.

01:00 This is the area of square B H F E.

01:04 Now, find the area of large rectangle A G D C.

01:09 Multiply side 12, by side 7.

01:12 That's the area of rectangle A G D C.

01:16 To find the area of the brown shape, we subtract areas.

01:20 Subtract areas of both triangles and the square from the rectangle's area.

01:28 And that's how we solve the problem!

Step-by-Step Solution

Let's first calculate the area of triangle ABC:

$\frac{6\times7}{2}=\frac{42}{2}=21$

Since the shape before us is a rectangle, we can claim that:

AC=GD=7

Now let's calculate the area of triangle HGD:

$\frac{7\times3}{2}=\frac{21}{2}=10.5$

Let's draw an imaginary line between B and H to get square BEFH where each side equals 3 cm.

Let's calculate the area of BEFH:

$3\times3=9$

Let's calculate the area of rectangle ACDG:

$7\times12=84$

Now we can calculate the area of the brown shape by subtracting the other areas we found:

Answer

43.5 cm

Related Subjects

The Area of a Triangle Calculating the Area of a Rectangle Area Area of Equilateral Triangles Area of a Scalene Triangle Area of Isosceles Triangles Rectangle Triangle Area of a right triangle Areas of Polygons for 7th Grade How do we calculate the area of complex shapes? How to calculate the area of a triangle using trigonometry?

Question Types

Area of a Rectangle: Subtraction or addition to a larger shape Area of a Triangle: Subtraction or addition to a larger shape