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Find the Area of Right Triangles, Other Triangles, Special Quadrilaterals, and Polygons

Show all work. For each shape, identify the base and height before applying the formula. Include square units in all answers.

Grade 6·22 problems·~40 min·Common Core Math - Grade 6·standard·6-g-a-1

Work through problems with immediate feedback

Recall / Warm-Up

What is the area of a rectangle with length 8 cm and width 5 cm?

13 cm²

26 cm²

40 cm²

64 cm²

Two lines that meet at a right angle (90°) are called what?

Parallel lines

Perpendicular lines

Intersecting lines

Congruent lines

What is the area of a square with a side length of 7 m? Give your answer in m².

Fluency Practice

An acute triangle has a base of 10 m and a height of 7 m. What is the area in m²?

$Obtuse triangle with base 12 ft, perpendicular height 5 ft shown as a dashed line outside the triangle, and slant side 8 ft labeled.$

An obtuse triangle has a base of 12 ft, a perpendicular height of 5 ft (drawn outside the triangle), and a slant side of 8 ft. What is the area of the triangle?

48 ft²

96 ft²

30 ft²

60 ft²

A triangle has a base of 9 in and a height of 4 in. What is the area in in²?

$Parallelogram with base 8 cm, perpendicular interior height 5 cm shown as a dashed line, and slant side 7 cm labeled.$

A parallelogram has a base of 8 cm, a perpendicular height of 5 cm, and a slant side of 7 cm. What is the area?

56 cm²

40 cm²

35 cm²

20 cm²

A trapezoid has parallel bases of 6 m and 10 m, and a height of 4 m. What is the area in m²?

Varied Practice

A triangle has area 45 ft². Its base is 10 ft. What is its height?

4.5 ft

9 ft

18 ft

22.5 ft

$Acute triangle with base 14 cm, perpendicular height 6 cm shown as a dashed line, and one slant side labeled 10 cm.$

The triangle shown has a base of 14 cm and a perpendicular height of 6 cm. The slant side measures 10 cm. Find the area in cm².

A trapezoid has $b_1 = 8$ ft, $b_2 = 14$ ft, and $h = 5$ ft.
Sum of the bases: ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ft.
Area $= \frac{1}{2} \times$ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ $\times 5 =$ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ft².

sum of bases:

sum in formula:

area:

A trapezoid has parallel bases of 5 in and 11 in, and a height of 6 in. What is its area in in²?

$L-shaped polygon with outer bounding box 8 m wide by 6 m tall. A 3 m by 4 m rectangular notch is cut from the upper-right corner, leaving an L-shape.$

An L-shaped polygon is shown. The outer bounding rectangle is 8 m by 6 m. A rectangular notch of 3 m by 4 m is cut from the upper-right corner. What is the area of the L-shaped polygon?

48 m²

36 m²

30 m²

24 m²

Word Problems

A triangular garden has a base of 12 m and a perpendicular height of 7 m. Fertilizer costs $3 per square meter.

What is the area of the triangular garden in m²?

How much will it cost to fertilize the entire garden?

A parallelogram-shaped tile has a base of 15 cm and a perpendicular height of 8 cm. A box contains 20 such tiles.

Complete the reasoning.
Area of one tile = ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ cm²
Total area of 20 tiles = ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ cm²

one tile area:

total area:

$L-shaped floor plan showing a 20 ft by 12 ft rectangle joined to an 8 ft by 6 ft rectangle forming an L-shape.$

A community center has an L-shaped floor plan. The longer section is 20 ft by 12 ft. The shorter section is 8 ft by 6 ft.

What is the total floor area of the community center in ft²?

A trapezoidal flower bed has parallel sides of 9 ft and 15 ft, with a perpendicular height of 4 ft. Mulch costs $2 per square foot.

Complete the reasoning.
Area of the flower bed = ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ft²
Cost to mulch = ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲

area:

cost:

Error Analysis

Theo finds the area of a triangle with a base of 10 m and a slant side of 6 m (the perpendicular height is 4 m). He writes:
$A = \frac{1}{2}(10)(6) = 30$ m²

What error did Theo make?

Theo forgot to divide by 2.

Theo used the slant side (6 m) instead of the perpendicular height (4 m).

Theo used the wrong formula. He should have used $A = bh$ .

Theo's answer is correct.

Amara finds the area of an L-shaped polygon. The overall bounding rectangle is 10 ft × 8 ft. A 4 ft × 3 ft rectangular notch is cut from one corner. Amara writes:
$A = 10 \times 8 = 80$ ft²

What error did Amara make? What is the correct area?

Amara computed the bounding rectangle area without subtracting the notch. Correct area: $80 - 12 = 68$ ft².

Amara used the wrong dimensions for the bounding rectangle. The correct area is 80 ft².

Amara should have added the notch area: $80 + 12 = 92$ ft².

Amara should have used the triangle formula instead.

Challenge / Extension

A composite figure consists of a rectangle (10 cm wide, 6 cm tall) with a right triangle attached to the right side (the triangle's legs are 6 cm and 4 cm). What is the total area of the composite figure in cm²?

A parallelogram and a rectangle both have a base of 12 cm and a height of 5 cm. A student says their areas must be equal. Is the student correct? Explain using the area formulas.

0 of 22 answered