Question

area of triangles and quadrilaterals
find the area of each.

1. 5.1 m 6 m
2. 9 yd 6.4 yd
3. 5.7 m 8 m
4. 2 yd 3.1 yd
5. 6 mi 5 mi 3 mi
6. 9 mi 6.6 mi
7. 7 mi 7 mi
8. 3.8 km 2 km
9. 2 yd 1 yd
10. 4.8 yd 8 yd 29.4 ft

Explanation:

Step1: Recall rectangle area formula

The area formula for a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width.
For the rectangle in (1) with length $l = 6$ m and width $w=5.1$ m, $A_1=6\times5.1 = 30.6$ m².
For the rectangle in (4) with length $l = 3.1$ yd and width $w = 2$ yd, $A_4=3.1\times2=6.2$ yd².
For the square (a special - case of rectangle) in (7) with side length $s = 7$ mi, $A_7=7\times7 = 49$ mi².

Step2: Recall triangle area formula

The area formula for a triangle is $A=\frac{1}{2}\times b\times h$, where $b$ is the base and $h$ is the height.
For the triangle in (2) with base $b = 9$ yd and height $h = 6.4$ yd, $A_2=\frac{1}{2}\times9\times6.4=28.8$ yd².
For the triangle in (6) with base $b = 9$ mi and height $h = 6.6$ mi, $A_6=\frac{1}{2}\times9\times6.6 = 29.7$ mi².
For the triangle in (8) with base $b = 2$ km and height $h = 3.8$ km, $A_8=\frac{1}{2}\times2\times3.8=3.8$ km².

Step3: Recall parallelogram area formula

The area formula for a parallelogram is $A = b\times h$, where $b$ is the base and $h$ is the height.
For the parallelogram in (3) with base $b = 8$ m and height $h = 5.7$ m, $A_3=8\times5.7=45.6$ m².
For the parallelogram in (9) with base $b = 2$ yd and height $h = 1$ yd, $A_9=2\times1 = 2$ yd².

Step4: Recall trapezoid area formula

The area formula for a trapezoid is $A=\frac{(a + b)h}{2}$, where $a$ and $b$ are the lengths of the parallel sides and $h$ is the height.
For the trapezoid in (5) with $a = 3$ mi, $b = 6$ mi and $h = 5$ mi, $A_5=\frac{(3 + 6)\times5}{2}=\frac{9\times5}{2}=22.5$ mi².
For the trapezoid in (10) with $a = 4.8$ yd, assume the other parallel - side length is not relevant as the value $29.4$ ft is likely a mis - write (if we consider only the given parallel side $a = 4.8$ yd and height $h = 8$ yd), $A_{10}=\frac{(4.8) \times8}{2}=19.2$ yd².

Answer:

1. 30.6 m²
2. 28.8 yd²
3. 45.6 m²
4. 6.2 yd²
5. 22.5 mi²
6. 29.7 mi²
7. 49 mi²
8. 3.8 km²
9. 2 yd²
10. 19.2 yd²