The problem is to calculate the area of the triangles labeled f, g, h, i, j, k, and l in the image.

1. Problem Description

The problem is to calculate the area of the triangles labeled f, g, h, i, j, k, and l in the image.

2. Solution Steps

Triangle f:

It is a right-angled triangle with base 2 and height

7. The area of a triangle is given by the formula:

$Area = \frac{1}{2} \times base \times height$

$Area_f = \frac{1}{2} \times 2 \times 7 = 7$

Triangle g:

It is a triangle with base 8 and height $1\frac{1}{2} = \frac{3}{2} = 1.5$.

$Area_g = \frac{1}{2} \times 8 \times 1.5 = 4 \times 1.5 = 6$

Triangle h:

It is a triangle with base 6 and height

5. $Area_h = \frac{1}{2} \times 6 \times 5 = 3 \times 5 = 15$

Triangle i:

It is a triangle with base 3 and height 2.

5. $Area_i = \frac{1}{2} \times 3 \times 2.5 = 1.5 \times 2.5 = 3.75$

Triangle j:

It is a triangle with base 8 and height that can be calculated using the length of 3 as a reference. Consider this as a whole triangle, we split it into two triangles of side

3. Since the two small triangles that create the original one both have a length of 3 for one of their sides, the area formula is base times height, times one half.

$Area_j = \frac{1}{2} \times 8 \times h$.

However, there is no height indicated for the entire triangle with side lengths of

3. We are given that the triangle can be bisected by a line of length

8. The sides are of length 3 on the outside edges so let us assume we should calculate the area for just one of the triangles with sides 3, 3, and

8. Since it is not specified otherwise, we will not calculate this area since there isn't enough information.

Triangle k:

It is a right-angled triangle with base 6 and height

1

0. $Area_k = \frac{1}{2} \times 6 \times 10 = 3 \times 10 = 30$

Triangle l:

It is a right-angled triangle with base 6.4 and height

5. $Area_l = \frac{1}{2} \times 6.4 \times 5 = 3.2 \times 5 = 16$

3. Final Answer

Area of triangle f: 7

Area of triangle g: 6

Area of triangle h: 15

Area of triangle i: 3.75

Area of triangle j: Insufficient information.

Area of triangle k: 30

Area of triangle l: 16